Hi,
I started my Phd 10 years ago, so some of my advice might be out of date, but here goes.
The first thing is that with a 2:1 you are unlikely to get funding for a Phd in a humanities subject. Not that you shouldn't try, but you should be realistic about your chances and look into other ways of doing it. As the previous poster said, the best way to start would be a MA. If you do well there, you can often get funding for a PhD. It's a question of proving to the awarding body that you are committed to studying and are going to do a PhD that will knock their socks off.
I also think it may be best for you to do it part-time, so as you can continue to spend time with your family, but still study (MAs and PhDs are fulltime jobs really). The tutition fees are less usually too that way.
I did my post-grad full-time, myself, but had to work for the first couple of years, since I only got funding for my last two years. (My nickname was Catita "three jobs" Inahatita) It was bloody hard work, I can tell you. I was exhauted most of the time. In fact, most people complain about the writing up bit; but of me that was the easiest thing as I only had that to to do by then thanks to the grant!
As for applications. Your best bet is to have a look at the politics dept in Durham and see what the specialities of the lecturers there. Hopefully one of them will tickle your fancy. Go to the library and read some of their stuff and identify some areas of interest for you. Also try and find some questions that you would like to find out more about concerning their work.
Then email them and praise what you read. Mention you are hoping to do a postgrad in their field and tell them that reading their stuff has prompted you to think about certain ideas and pop your questions. Hoepfully this will get a email discussion going, from which you can ask for an appointment to discuss things further.
Ar said interview try and come prepared with ideas for a research project, but don't worry if you very vague. Tell them you would like their expert advice about how to go about it. This should get them suggesting things to you willy-nilly. believe me, academics always have four or five pet projects they want to do, but have no time for and will be more than happy to see a student do some of it for them.
Hopefully by this point you may have captured their interest enough for you to broach the question of the possiblity of their supervising you.
Once you have a supervisor in the bag, then do the applications. That way it should a sure fire deal.
A long-winded process I know, but it can pay off. I promise.
Good luck with everything.