MrsSnape, it is hard as buggery to get a place on HB but it can be done. I got ours advertising privately, 4 years ago - I put an ad in the paper, you know, reliable single woman looking for a house, guarantor etc...(that helps) and got a few shifty replies but eventually my very laid back landlord and his laid back house - Ok it was a heap, but it was workable and we're still here
I've looked around since, and a few agents are happy to consider/put you forward, if the house is messy or scruffy and needs work, hasn't been recently refurbished or whatever...especially if you have someone to act as guarantor. My dad does this though he's never had to pay out...we get HB straight into the bank, it's paid in arrears but we cover it and it goes to landlord as a standing order monthly, so they don't have to wait.
A lot of LL's have a type of insurance that excludes people on benefits. which is just shit basically but what can you do...it might just be a line I've been fed by estate agents though!!
Yes, to answer OP, you can get it paid direct to you but you'll still have to let them know especially if through an agent, as they will ask I expect - mind you, if it's a private rental, maybe you could get away with it! Risk of being chucked out though if they sprang you...