You first need to ascertain the thread of the BB where it screws into the frame , almost certainly but not def. English.
The next thing to determine is the interface between the BB and the crankset. e.g.Square which it most probably is.
The width of the spindle must also to be assessed (should be stamped on your existing spindle) to ensure clearance of the chain stay and conversely to avoid a too far apart pedalling action.
I have a couple of old chainsets you could have if you pay P&P but they are not hard to source on Ebay
"Probably". Assuming it has cotterless cranks, the chances are it has a standard BB shell width and thread, and something modern will just screw in
*That said*: I replaced the BB on my Coventry Eagle (believed to be early 80s) the other day and found that the rivet holding the derailleur cable guide on intruded so far into the bottom bracket shell that I couldn't get a cartridge BB in there until I'd removed it. Not a problem for me because I was fixifying the bike at the same time, but if you will still have need of the little bit of plastic then you might just want to check you either don't have the same problem or can obtain a replacement cable guide
Thanks guys, and cheers for the offer Genman, but I do have a perfectly functioning double chainset - just looking into getting a knee friendly tripple on my winter bike, but by no means 100% going for this yet as I may find it easier to just use a larger cassette ratio.