If you can demonstrate good programming skills I think most companies would still hire you even without past job experience (I assume that's what you mean by portfolio - if you mean Github projects then in my experience nobody really looks at those).
A CS degree is also irrelevant - pretty much all programming jobs in the UK just want any technical degree. In all the companies I've worked in most people did maths, physics, engineering or CS, but CS was still a minority.
If you can program well then the real difficulty will be getting your CV past HR since they probably will dismiss it based on lack of experience. I'm not sure how to solve that but asking here seems like a decent thing to do.