aarghh! Cat keeps typing!
Ok, the problem with getting housing benefit on a private rental is that the landlord has to wait a couple of months for the council to start paying him, and they don't stump up for the deposit. If you can afford to rent a place off your own bat and then apply for HB, it works more smoothly. Many landlords/agencies automatically reject tenants on benefits (insane IMO, the rent's guaranteed!) so this will all very much depend on where you are.
Where I live, one of the letting agencies actually specialises in lettings to tenants on benefits so that was a godsend. You should try to get a benefits adviser assigned to you - they vary in quality (basically, if they make everything sound like a problem they're not very good), but at least you'll find out what forms you need to fill in.
A better option for benefits advice is the Citizens Advice Bureau (CAB). Again, how quickly you can get an appointment depends on where you are.
You can also look into refuges. They're all right these days, though obviously quite an emotional environment. Start by phoning Women's Aid.
Get a social worker assigned to you as quickly as possible. Once you're getting social care (or whatever it's called), you will then have access to unbiased advisers who can help you with all this stuff.
As well as the emergency loans, Social Fund has money it can give out for buying necessities when you move in. You don't get much tbh, but mine was enough for me; I got everything from Freecycle and Ebay.
You will qualify for at least jobseeker's allowance, child benefits, housing & taxes. Hardly a fortune but you can live on it
Best to bring all your financial, tax & pension stuff with you - there are reciprocal agreements with EU countries, but I don't know what they are. It's even possible you might get more for a while, if social benefits in your country of residence are better.
You normally have to wait about 3 weeks to get any money. But they do have those emergency loans.
Make sure your car is legal & insured for the UK. The last thing you need is a bloody great traffic fine!