The 1401 was more of a service processor for a mainframe. You could use a 1401 to order jobs and manage card sorters and things of that nature.
The 1401 was occasionally sold as a standalone accounting machine instead of a service processor, but never as a mainframe unto itself.
It's more of a minicomputer than a mainframe. Which should say everything about its era. "Mini" meant only like, six racks of gear.
I learned FORTRAN on an IBM 1401. Our intro chemistry professor thought it was a good idea to incorporate IBM's FORTRAN programming coursework into our chemistry lab. I wasn't so good at chemistry but excelled in programming and so earned a decent chem grade. In the years that followed I used the FORTRAN for numerical analysis classes. It all led to a career in programming.
What's crazy is it's so unknown to the general populace. Kids learn about George Washington and Bill Gates the businessman who gave us Windows, but they have no clue who Ken and Dennis are. Punch cards are meaningless to them. They wouldn't know an old hard disk from a vinyl record box. But one day they will. One day people will realize that this was the beginning of humanity. The real beginning. The PDP-11, the 1400 series, the ENIAC.
If you haven't been to the computer history museum, go!
It's important, but let's not engage in hyperbole.
I suggest Jay Moseley’s excellent site on MVS system generation  or get Jürgen Winkelmann and Volker Bandke MVS Turnkey installed system ready to go .
It had a Cray 2 just sitting there, gathering dust. I loved the look of it. I think eventually they sold it just to make room.
I started programming professionally back in 1990 on IBM mainframes. I used to daydream about buying an old machine to run in the basement. (But shortly after the 386 and 486 machines started hosting emulators that allowed mainframe programming on the desktop. My burning desire for a home mainframe died out.)
Unless I'm mistaken and they both let you do stuff on the computers, which would be cool.
The Computer History Museum in Mountain View California has a few old computers running, but is mostly a display museum.
At the Living Computer Museum I logged into a DEC-2060 on a VT100 terminal and amazed my younger friends by navigating around the system and firing up a few ancient text based games. Being of the hacker mindset, I also showed them all the information you could get about logged in users prior to logging in from which one could have used to guess account credentials back in the day...
Explaining and demoing the COMND JSYS was quite fun. The COMND JSYS provided command line parsing and completion, one of the predecessors to t-shell, bash, and other shells with completion. I had a great time revising the past and highly recommend you visit with an old-skool programmer.
For those who are curious you can read about the COMND JSYS on page 164 (chapter 3, pg 52) of the following document
The thing needed a 220V outlet, sounded like a jet turbine, and probably drew a few thousand watts. And it was less powerful than the i386 desktop I had (running early Linux).
It's a neat idea, but not practical or pleasant.
One thing, unique at the time I think, was you could selectively hide rows and then perform column operations on just the visible ones. Very handy when you needed it!
removeable disk packs were always a problem due to head crashes.
my point is, every computer had downtime due to poor reliability, when evaluated against what we have today. and most things were not 'user serviceable', unless your user was highly skilled in electronics, test equipment and digital logic.
In my field, once we moved to SGI's you started to see the salesman a lot more than the FE because the machines were so reliable. And today it is all commodity parts that anyone can cheaply swap-tronix things back to operational.
I give the computer museum credit for keeping this history in working order.
The original VAX systems, occupying 2 to 4 cabinets, were similar to the 1401. They were both "mini" computers -- smaller than a mainframe, but considerable and interesting unto themselves.
The microvax was a VAX re-implemented with much cheaper, cooler logic, so it could be sold as a desk-side or a single rack system.
It has so many things to look and interact with.
Most notably the Colossus, Bombe, Acorn computers and BBC micros.
If you are visiting as a tourist it's not too hard to get there from central London by train or car.
I take it you noticed the "politics" of Bletchely Park trust and TNMOC. Its sad that the two organisations fight over the heritage of that place.
If you read computer magazines from the 70’s, machines that we would call desktops were very often referred to as mainframes.
But “mainframe” was exclusively used for big batch and time-sharing iron sitting in a “machine room” that you weren’t allowed into unless you were employed as an “operator” or the IBM serviceman doing scheduled weekly PM (preventive maintenance), during which time no jobs ran.
In return, I will respectfully disagree with you, and back up my assertion with the following citations:
"Don't worry any more about wiring hundreds of wires in your Altair to expand the mainframe" - Byte Magazine, October 1975, page 21
"Need Altair IMSAI/POLY 88 mainframe, memory or what-have-you." - Byte Magazine, January 1977, page 98
"Our modular systems use common Vector 3 mainframes, boards, and printers." (Vector was a Z80A desktop computer that ran CP/M) - Byte Magazine, December 1980, page 89
"Z80 CPU, 4 Mhz, with one serial port; 12 slot S-100 mainframe, disk controller, 64K Dynamic Ram, CP/M 2.2... $1,645" - Byte Magazine, December 1980, page 156
"The OSI Challenger is the only completely- assembled, ultra-high-performance, fully-expandable mainframe computer that does this much for this little" (The OSI Challenger was a desktop computer) - Byte Magazine, November 1976, page 19
"MERLIN (trademark of MiniTerm Associates) is a new concept in peripherals modules for mainframe microcomputer systems." (Merlin was a dumb terminal for IMSAI and Altair desktop comptuers) - Byte Magazine, November 1976, page 64
"That's why we offer three mainframes including the Altair 680b, Altair 8800a, and Altair 8800b; ten peripherals including a multi-disk system; and over 20 plug compatible modules including our new, low power 16K static memory board." - Byte Magazine, December 1976, page 17
As I stated, it wasn't until the 1980's that "mainframe" changed to only refer to big iron.
It seems to come from microcomputer hardware and accessory companies trying to throw the word "mainframe" into their ads somehow and make their stuff seem more important.
"Model 706 mainframe can accomodate 10 scanner plug-in cards. ... Before operating the Model 706, the appropriate scanner cards must be installed into the mainframe. Each scanner card (up to 10 cards per the Model 706 malnframe) is Installed in the appropriate vertical slot In the rear panel of the Model 706. Refer to Figure 2-1 for an overall picture of scanner card installation." https://archive.org/details/keithley_KEI_706_Instruction/pag...
"Peripheral cards, capable of handling words as large as 32 bits, perform operations normally requiring expensive computer mainframe expansion — display control, multiple capstan tape control and the like." https://archive.org/details/TNM_832_Data_Interface_-_ECG_Dat...
However, that isn't what reaperducer referred to when saying "the term “mainframe” seems to have become exclusive to big iron only in the mid 1980’s."
Here's an MS thesis from 1971 titled 'The minicomputer : an educational tool', which makes considers the "mini-mainframe" as a distinct category. https://archive.org/details/minicomputereduc432mars/page/62
Here's how a 1974 publication titled "Role of the Minicomputer in Small Educational Institutions" characterizes minicomputers, quoting https://archive.org/details/ERIC_ED100376/page/n3 :
> What is, a minicomputer? Unfortunately, the term minicomputer is used by many people with many different meanings. For the purpose of this paper, we shall characterize a minicomputer by the following two criteria.
> (1) Physical size . Typically, the main components of a minicomputer (its CPU and main memory) are closer to the size of an electric typewriter than, say, a washing machine. (Not counting the power supply and racket, the CPU and memory may fit on a single printed circuit board!)
> (2) Cost . Typically, the main components of a minicomputer (its CPU and main memory) can be purchased for less than $10,000 - in some cases for less than $1,000.
This is clearly more like a machine we would call a desktop - how many people have washing machine-sized computers on their desktop?
A 1975 report titled "Use of Minicomputer Facilities for Higher Education Instruction" helps identify that 'minicomputer' was a new computer category starting in the late 1960s, quoting https://archive.org/details/ERIC_ED112763/page/n3 :
> Although each of the methods offered a level of computing suitable for some instructional use a belief was expressed in 1969 that the new "minicomputers" might be able to provide instructional computing support that even the smallest colleges could afford.
I suspect you're misinterpreting what you are seeing, those adverts probably showed someone working at a keyboard and VDU screen. They aren't the computers, they are just terminals which connect to the computer. Have a look at the links below for some examples.