HG, as someone who's got an old custom steel frame collecting dust in the basement...
is it really that simple?
Early 1980s will be 5-speed. Can you spread the drop-outs enough to accommodate 9-speed, which I think is still available in Ultegra? Would it be better to go to 10-speed, bearing in mind that a cassette won't last forever and 9-speed may not be available forever; and if so, can the drop-outs be spread that far?
And for you, as well as Margo and Deb if they're listening: does spreading the drop-outs weaken the rear triangle or cause chain alignment issues?
Bearing in mind that you'd have to replace at least the rear hub, can it really be done that cheaply? Or are you talking about parts only, and building the bike herself, just going to a framebuilder for the cold-setting? Little things like chain, cables and handlebar tape add up...
ETA: and what about the front derailleur? If it's a clamp-on, will a modern front derailleur clamp fit narrow Reynolds 531 tubing? My old frame has a front derailleur braze-on - so am I right that that limits what gearing I can put up front?