I think you should tone it down a bit with the governement paranoia, yes it is true that the governement knows what we do but reality is we can't do anything about it. To me it sounds like the money you're trying to convert to bitcoins is illegal. Because if it was legal you could just buy bitcoins through localbitcoins like alot of people do. Since you live in the UK and not a random country like Uganda or any 3rd world country, I believe you can use exchanges and just buy bitcoins normally. Also we already gave you some tips on where to buy bitcoins, but honestly i don't think that anything you do will be 100% anonymously. Even if you use tor or any vpn, if a government wants you, like the US, they WILL find you. It doesn't matter what anyone says, nothing is 100% anonymous in the internet.
You can hide yourself for some time but eventually they will find you. The internet was made by the army, you don't think they have the keys to the backdoor?
just buy bitcoins normally and don't try to find a way which is 100% anonymous because there isnt one. Just being realistic here.