You can go to firms that specialize in incorporating shelf companies which are commonly known as formation agents. To register a company in the UK you need a local director address and a local company address (which are usually setup with an international mail forwarding service) as well as some other requirements most importantly a business bank account which under UK/EU money laundering regulations isn't trivial to open (And with a thin credit file almost impossible to open in the UK without a large deposit and a good formation agent).

Depending on the type of company you are registering for the prices can range from a few 100's pounds (plus fees/deposits) for a regular limited company to considerably larger sums if you are buying/forming a shell corporation.

Another good reason to get a lawyer (in both jurisdictions) is that some countries also have regulations regarding owning foreign companies. If your business is in a regulated field, health care, finance etc. this usually tends to complicate things even further.