I've been wondering, is it common practice to offer someone a PhD place (albeit a non-funded one in my case) WITHOUT being asked for an interview? This has actually happened to me (I did submit a proposal of my own) and although I was happy enough at first I am now somewhat concerned about it...

Is it possible for an admissions department just to team you up with a certain supervisor with similar research interests (again this happened to me) and leave you to sort out the details on arrival to the University?

It does sound a bit strange. At the very least there is a telephone interview (if the student is from abroad). In my case I was invited to fly to the Uk for the interview and they paid for it.
Then again, there are probably not so many people out there who apply for a non-funded PhD so they'll be happy to get what they can.

It is probably true that most universities will take anybody with the right qualifications, if they fund themselves - they are selling a service and if you look like you're capable of completing it on paper the interview would ordinarily be a formality.

Not having an interview at all does seem worrying and might lead you to question your new supervisor’s commitment to your research proposal. For a start it means that you don't get a chance to see if you like your supervisor or your new working environment. It gives you no chance to find out what facilities will be available to help you in your research.

You should ask to visit and meet your supervisor before you accept their offer. The chances are high that other institutions will be happy to take you. Depending on the nature of your research the university you choose does not even need to be in the same city (although you will need to meet your supervisor every few weeks).

I am also doing a non-funded PhD and I didn't get a formal interview. But I am doing it in the same dept i did my masters and he asked my previous project supervisor about me. So they wouldn't give it to just anyone.

I wish I had been as fortunate. I`ve applied to various universities for a self-funded PhD and have been rejected without even an interview. Be happy that you have got a place!

Wow! That sounds great - I've often wondered if you could get on to such a thing without an interview!! What did you apply for and where? I would go for it as you very rarely get to do a research project that is entirely yours so it's something you really want to do! But it is important to meet your supervisor(s) to make sure you get along (except you won't really know until you get there and work with them so it's worth checking it out!