Hmm, tricky one! Best I can think of, considering Skinners and Autarky are out, is WorkingHPRs duck & potato - it's £53 for 2 x 15 kg, so a fiver a sack over budget, but it's grain free so might help get some weight on since there'll be less waste. Or if the budget is strict, then CSJ Complete Tripe - it's £20.80 a sack, and has a shocking amount of grain, but it's wheat free at least, and the tripe might help pack a bit of weight on.
And of course, as you know, raw can be dirt cheap is sourced right so that might be an option.
When my greyhounds came to me they were very underweight and I used Lactol (puppy milk) to help bulk them up and it worked well, combined with four small meals a day. That might work out to be a bit out of budget for your friend though?
Hope you managed to find something, let me know if you do! Also good to keep up to date with the budget options available