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An older Shimano 6/7/8 speed Hyperglide hub will be 126mm and won't have the long weak axle problem that I think @mdcc_tester is referring to. 7 speeds will definitely fit. There's a chance you might squeeze all 8 gears into a 126mm space, but I've got a feeling the bottom gear might be too close to the stay. Bankrupt Bike Parts keep a stash of those hubs.
Jonny69-
older Shimano 6/7/8 speed Hyperglide hub will be 126mm
8-speed will be 130mm. Many of the 6/7-speed freehubs (and even some 8-speed, but you'd have to go looking for them) will be UG not HG which makes finding a cassette a PITA, although UG/HG hybrid 6/7-speed is pretty common and eliminates that issue. Nonetheless, widening the rear end by 2mm per side is much the best approach because there's plenty of choice of ratios and price points with modern 8/9/10/11-speed cassettes.
gbj_tester
Hmm, that's an option. I'm trying to keep this fairly budget as I'll be getting something much more modern in the not too distant future. Any suggestions?