Would it be possible for the UK Prime Minister to defect party?

There is no written law about this so I can only conjecture from established custom. There isn't even a law to say there has to be a Prime Minister. It's just that there has always been one since 1721, so we've got used to the idea that there MUST be one. So we don't elect a Prime Minister, we elect the House of Commons, and who is Prime Minister follows from the result.

If Cameron did that, and there is nothing in law to stop him, the Conservatives would still be the largest party. The Queen then has to appoint a new Prime Minister. It's a royal appointment, and that's why a new Prime Minister always has to visit Buckingham Palace after an election, so he or she can be appointed in person and "kiss hands". No, there is no kissing of hands, it's just the name of the ceremony!

In theory, the Queen has a free choice, but by convention, she should appoint someone most likely to command a majority in the House of Commons and lead a stable government. This is what she always does, and usually it's obvious who that should be, so you don't notice that that's what is really going on. She would have to sack Cameron and appoint someone else, as there is no way he can continue to be Prime Minister as part of a party with only two MPs.

Bearing that in mind, it would be exactly the same as if Cameron had resigned for some other reason,

maybe even that he just feels it's time to go. Harold Wilson did that in 1976, and Tony Blair in 2007. All that happened was that Labour chose a new leader, and that's who the Queen appointed as the new Prime Minister. There is absolutely no need for an election.

The only sources I can give for this are respected books on the workings of British government such as those by Bagehot and Dicey, as it's not formally written anywhere.

I am sincerely thinking of defecting the UK. I'm sick of being in a third world country.

The PM is an elected Member of Parliament just like any other party member(MP) and so could resign but they would have to resign his seat, meaning the seat for MP would be up for an election, the deputy prime minister would take over temporarily as PM and it would either be decided by the party he/she would be PM or a new PM would be elected by the party. There would not be an National election, just a local by election for the vacant seat

Y'mean like Blair did?

It's possible but unlikely to happen.

Certain parties are defective, yes.

CAMERON ISNT EDUCATED ENUFF TO JOIN GREEN PARTY