Well the debt would become part of the 'estate', so yes it would be wiped. Having said that, it is very unlikely that you would be able to stay with that letting agency.
You might find that you also struggle to find a letting agency that will accept you, to be honest. They normally need references, etc. and previous unpaid debt is not a good start.
Having said that, you need to be aware that the ORs take a very dim view of 'favouring creditors'. This means that you can't stop paying everyone else so that you can pay your debts to your landlord to avoid eviction, because it is favouring your landlord.
You also need to know that it is illegal, once you declare bankruptcy, to pay ANY debt that occurred prior to bankruptcy, even to relatives and so on. It is all officially the 'possession' of the Official Receiver.
You really do need to get professional advice. People can and do rent after bankruptcy, but obviously like everything, it is harder to enter into any financial contract for some time after you file bankruptcy, because the bankruptcy order is basically a sign in the sky that you cannot meet your financial committments.
I am not being harsh, btw. Just very honest. I have been discharged since October 2007, and it has been the best thing I ever did, but I went into it with my eyes wide open.