The Copyrights, Designs & Patents Act 198 has "fair dealing" clauses which specifically permits back ups (Section 50(A)) and time-shifting (Section 70). I'm not aware of any case law that limits these permissions; the Copyright & Related Rights Regulations of 2003 does forbid you from circumventing a technical protection measure, which is in opposition to CDPA.
SS50(A) in CDP as amended refers to backups for computer programs. I'm thinking backups of media, DVDs, CDs. Time-shifting is allowed as you note but it limits you to view a single recording a single time, so you can watch a recording of a TV show but you must never "deal with" the copy once you've viewed it; moreover this only applies in domestic settings.
To consider UK "fair dealing" anything akin to US "fair use" is to not understand the scope of either IMO.
At the moment "format shifting" (but not time shifting) is still illegal, but no-one enforces it and it's going to be changed. (I haven't kept up; maybe it has already changed.)
As you say, being allowed to make backups is tricky if you're not allowed to circumvent technical protection measures.
