This 1994 legislation made it the law that plugs must be fitted to certain consumer devices: http://www.legislation.gov.uk/uksi/1994/1768/contents/made
Before that time, almost everything (certainly everything I purchased) came without a plug and you had to buy a plug and wire it yourself. Probably because these things are expensive, and costs could be reduced by leaving them out.
I'm not certain on the exact motivation, but I think it's a mix of preventing people doing it wrong, and better mechanical properties (especially strain-relief) of moulded plugs.
It's also required now that the live/neutral pins be partially insulated (the 1/3rd closest to the plug or so) to prevent shock hazards to people curling their fingers around the plug when inserting or removing.
I remember us having to wire up kettles, lamps, and irons when I was a kid. And you'd sometimes go to antique (or second hand) shops and come across old appliances that had no cord attached. Anecdotally, we bought an old style telephone that we then had to wire back up.
That being said, I can't corroborate any claim that this was backed by legislation.