Hi there,
Graham is quite correct, there are generally no problems with non-uk residents operating a business in the UK. However the government does impose some restrictions on certain foreign nationals from time to time.
I would like to add though that you need to be clear that a sole trader is very different to a registered company in the UK. A sole trader can simply operate their business as they wish (within reason) and have little administrative responsibility. A limited company (i.e. registered) however, has greater responsibilities in its operation, administration and reporting. I could write reams on this subject but just wanted to make sure that you understand that the two types of business are very different.
Mike.
