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Thanks for all the answers. I'll keep this short and sweet, as I'm using my phone...
The offer letter I was given, mentions absolutely nothing about "subject to references", I've read it over and over again, and it just has details such as my start date, hours and salary. I got my ex employer to phone them, and he told them he was happy to give me a reference over the phone, off the record, as it was all supposed to go through the HR department. They told him this wasn't acceptable and that he "could be anyone on the other end of the line". Jesus. Talk about paranoid.
I've since found out today, that I took a couple of large clients from them during the year, which would have been quite a major loss to them. I'm starting to wonder if this was a personal thing. Even the agency have said its not something they've come across before.
If the letter had mentioned the offer was subject to referencing, then there's no way I would have handed in my notice. There's no chance of me getting my old job back, either.
I've got an interview on Friday, but the job doesn't start until January. I'm trying to remain positive, but its very hard right now. Things have just gone from bad to worse...