Appreciate this is in the realms of thread drift here, but worth saying - I think - because most people (and I am sure most students) are unaware of the implications of recent changes in air law.
If I was going to set up a university flying club - a club to encourage people to fly, rather than as some back door way into a CPL - then my plan would be this.
Get a member with a microlight licence and try to find someone who will let you use theirs. (Possibly renting it, now that rental is allowed for factory-built ones.)
Set up a stand at Freshers week, and sell memberships for £50 a year which include a flight. (Introductory Flights for cash are now allowed in light aircraft and microlights by non-instructors as long as the club is not-for-profit and the pilot doesn't get paid).
Identify future pilots from the Introductory Flight gang and then get them trained up. There are scholarships available - at Strathaven, for example, we have had teenagers get £3k, 2 x £1k and some other sum from the BMAA alone. And then our not-for-profit airfield also has two annual £2.5k scholarships.)
If you go the microlight route, then ideally over the years start getting some students trained as instructors. Quicker and cheaper than the light aircraft route.
Basically, that's how the Edinburgh University Hot Air Balloon Club operated when I was club secretary back in the early 1980s.
So, where do you get the cash to buy an aircraft? Well, there would be a fair bit of cash around if you sell 100 Introductory lessons at £50 each. Perhaps you might sell 200 or 300? Try some crowd-funding?
And then find an airfield that is going to do you a deal on hangarage and landing fees. We, as I have mentioned before, would be happy at Strathaven.
Stay Permit to Fly and you can do your own maintenance.
Who says you have to be part of the Sports Union - although handy for all sorts of things, like minibus hire etc. Just do it!
(and rugby etc are VERY capital intensive - just think of the land value for housing! As many unis like Glasgow and Edinburgh have already done.)
I can't think of how many students there are in central Scotland. There are 235,000 in the whole of Scotland. Is it impossible that one could find 40-odd to put up £250 each to add to the Intro Flight money and buy an all-metal Zenair 601 light aircraft? Would be a great way to build experience taking up Intro Flighters for the cost of the fuel - and with a Rotax 912 that would be around £7 for a 30 min one.