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You could visit your Local C.A.B They will have an up to date list of all the Private Landlords in that Area, and not every one wants a huge deposit, my daughter didn't have to pay one. Good Luck
Also the Agency I rented from unusually charged no "admin fee" and it was just the deposit and first months rent.
This is a rarity today
We are in our 3rd rented property since 2007, been upfront with all letting agents and they have all insisted on doing a credit check - procedures! we fail but still we have to pay for the priviledge, £120 for 1 applicant. Hence a property can only be in my name.
1st landlord wanted, and got, 6 months plus 1 month in advance. Seems to be the norm 6 wks deposit plus a months rent, it has been to the agents we've spoken to, we were asked to pay £200 more for having cats, no one asks more for having children though! We havent, but they can be just as destructive.
Anyway hopefully you won't have the same problems, good luck.