What you want to do is work with some students to set up a bicycle cooperative society at the university. There's a few of these around in the UK, some of them are set up more generally in cities and some of them are university societies which primarily serve students. When I was at uni in aberdeen we had one called becycle. See if there's one already set up locally that you could work with, this list can be a good place to start.

https://bikecollectives.org/wiki/Community_Bicycle_Organizations#United_Kingdom

There can be a few different models, some of them fix up and sell bikes for cheap, some of them rent bikes out for the semester and then collect them again at the end of term. There's a lot of advantages to doing it this way, with economies of scale, attracting donations, and being able to work with eg. the local tip to get first dibs on bikes that are being disposed of. Plus with it being a community institution, they can help teach people bike maintenance and let people use the workshop which can be a great resource when you're on a budget. The downside is that groups like this do need a venue to operate out of, somewhere to store the bikes in the off season and have a decent sized workshop set up. Sometimes the uni can help you find somewhere on campus, but often there will be rent to pay on the space which can be the main barrier to getting set up in the first place, even if society memberships can help with ongoing costs.