I understand your hesitation to take on this task yourself. I know many people who have bought pre-built or had a friend put their stuff together because they lacked the confidence to attempt it themselves - and that's completely okay. I know of several UK sites/places that put a computer together based on your specifications, however - finding one that does this for parts in your inventory will be tricky and big companies will not do it for you because your parts could possible be DOA and they would not want to take liability for that.
Some ideas:
Do you have a friend who could do it for you? You might need to buy him a beer to get him to agree
Do you live near a university? Maybe get some electrical/telecom engineering student to put it together for you for pretty cheap?
Some small local computer shops might do this for you. I know I used to charge 50-100 pound per build when I was a student.
Some issues:
Be aware that if you ask someone else to do this for you and they damage any of your components, you may have a hard time trying to prove that the said item was not DOA.