Who owns the intellectual property for work you do on weekends?
To broaden Bill Barth's answer a bit: you definitely need to get an lawyer involved.  You also should make certain that there is date-stamped written communication ensuring that your university's legal/IP staff are aware as well.  This may seem like a pain and may make it harder to get started on anything, but it's much better to get any possible conflicts identified and sorted out now, rather than to find yourself in the middle of a complex and lengthy lawsuit later.

I don't know about the UK, but suspect it to be similarly heterogeneous to the US, where there is an exceedingly large range of differences in the IP rights given in employment agreements at research institutions, both within academia and outside of it.  Some places are very liberal and basically claim nothing that's not "in the direct line of your duties."  Others claim even your dreams and the photos you take at your kids' birthday party (not exaggerating!).  In all cases, however, there is often a wide grey area between de jure and de facto policy, and it's important to get an agreement and understanding written down before you give IP to any second organization.