Think you need to explore this more with the University about the accounting for these companies. Entering companies in your name with the University potentially holding funds for research may be something they do on a regular basis, but you need to understand exactly how this would operate.
The comments I post are personal opinion. Always refer to official information sources before relying on internet forums. If you have a problem with any organisation, enter into their official complaints process at the earliest opportunity, as sometimes complaints have to be started within a certain time frame.
I've asked the university for clarification, though it is a standard practise. It looks like I'm going to have to try and find a solicitor who can provide watertight legal advice (if that's not an oxymoron!).
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Thanks for everyone's help and advice. 😀