Getting off joint mortgage

If your boyfriend's only just divorced, he's got himself financially enmeshed with you pretty quickly.

There is no quick, cheap way of getting off that mortgage. You say he's "just divorced". Courts favour a clean break these days, so if he's still on the mortgage then I would be very surprised if his ex wife is able to take on the mortgage. If she was in a position financially to do so, it's less likely to have been part of their agreed Consent Order. And as the divorce was so recent, I would assume nothing has changed in her position. It's the first thing to check, but seems unlikely.

Half his salary to house and maintain two children could very easily be a fair settlement - especially as he's most likely retaining an increase in equity in the property. The court would not have left him without enough money to house himself (though as there were 2 children to house too, he may only have had enough to house himself very basically)

How amicable are things with his ex wife?

I'd say the very quickest solution here is that he simply asks her whether he can temporarily reduce his payments. I'm divorced - legally I'm entitled to about £400 a month from my ex in child maintenance but I've never claimed it. If things are amicable and she can manage for a couple of months she may be prepared to accept the reduction - either through trusting him to pay it back, or if it seems unlikely he can, by him offering sacrifice some of his equity. So I'd check that option first.

Next possibility is to see if she would agree to (and a lender agree to) a remortgage that would release equity. Is there any? Then he could take cash out of the house, commit to paying the new higher payment (or same if same term) and agree a different equity split with her.

If that doesn't appeal or no equity, he could look at extending his mortgage or going interest only for a short period. Actually, I should have put that higher up the list of possibilities - to take a mortgage payment holiday (beware of impact on credit rating) or a period of interest only, to reduce his outgoings so he has more for both your rent.

Next option - although renting is awful for security in your situation, it's good for flexibility. You have been supporting him, no he can be supporting you - from the money he has, can he afford either a houseshare with a double room that you can share as a couple, or if not available, two single houseshare rooms?
If you've been renting a whole place together plus all bills, then a shared room in a house share is going to be loads cheaper.
At the same time, you can get any job you can which will help.

He must have been living somewhere after his divorce - was that a house share? In which case, he needs to go back to what he can afford. Or if he was with family/friends, try to do that again and use the money saved to house you in the cheapest house share you can get.

I know it's not ideal - but all those options are going to be more realistic than getting him off the mortgage, given that the ink is still drying on the CO so their circumstances presumably needed that solution.

I hope you find a job quickly!

And don't forget to talk to Shelter / your local council for advice if you're facing homelessness. For a start, if you can't pay your rent it will take your landlord time to evict you for that. If you think you have 2 months before the money runs out, then you have 2 months plus the eviction period. Is there any reason why you wouldn't get a job in that time? You could take advice on other boards here (and from Shelter) on what priority bills (rent & council tax I think) that you should pay, and how to handle temporarily stopping other payments, like credit cards if you have those.