Also, I have found out the qualifications for Prime Minister. They are:
1. You have to be the leader of the ruling party/party coalition.
2. An elected Member of Parliament.
3. Be a minimum of 18 years old.
4. Be a citizen of the UK, Ireland, or the 52 other Commonwealth Countries.
So you technically can be born an American and become Prime Minister. The easiest route would be to find the nation with the most lax citizenship requirements, then moving to a reliably conservative district in the UK with a really,really,really old MP.
That and many cosmetic changes to appeal to other Brits.