Hey Enrique, as a fellow programmer it's awesome to see you're interested in CS based work experience! I personally was able to do work experience with the Raspberry Pi Foundation, commuting from London to Cambridge each day. If commuting doesn't really suit you then you could try places such as SalesForce, Accenture, BT, Thomson Reuters, Kano etc which all have offices in London and have taken on work experience students before. Or, have you maybe thought about ringing some of your local computer repair shops to see if they'll take you on? I was able to shadow someone who built custom PCs over the summer and it definitely helps with the hardware side of the CS course.
Hope this helps!