Just chiming in to agree with Paul. I've interviewed many hundreds of graduate software engineers over the years (and probably hired 100+ too.) Never met any hiring manager who cared about which university you went (note this is not the same in all degree subjects - if I'm hiring electronics graduates, I do care about which university because some courses are way better suited to what I'm looking for than others.)
What matters far more is what you have done/can do. If your CV has a link to some great work on github, some open source project you've contributed to, some app you've built, some snazzy websites (if it's a web developer job) then that counts for far more than your degree - particularly if it's stuff you've done in your own time, rather than because you had to do it as part of your course.
If you have good 'A' levels, that will be visible on your CV. (And if you do have good 'A' levels, many Russell Group universities will have Computer Science vacancies available through clearing/adjustment in August anyway.) That said, if you do go down the work & study part-time route, a qualification from the OU is generally ranked pretty highly by employers - it shows someone is pretty committed. Takes a few years though.
In my experience, it's pretty easy for good software people to find jobs elsewhere in Europe, in the US etc. if that's what you want.