Change to the Signed Tenancy Agreement

Tenancy Types and Management

I very stupidly signed a Tenancy Agreement which had me as LL residing at the Letting Agent rather than my home address; it then went on to say that each months rent would be paid to the Agent. I want it paid direct to me as it has always been in the past with previous tenants.
The Letting agent has admitted they made a mistake in thinking they were going to manage the property (I signed "Tenant find only" on their "Services Agreement") and are, I understand, although not returning my calls nor emails, going to return the management fee they have deducted out of the first months rent. My question is, is it possible to get an addendum to the original AST or do I have to just take it on the chin and accept that the rent gets paid to the Agent every month, they'll take a fee and for however long it takes them send me the balance each month?
I'm sure the new tenant would have no problem with it coming direct to me and obviously the tenant would also have to sign the addendum.
Lesson well & truly learnt not to sign anything in a hurry-the AST was sent to me the evening before the tenancy started!
TIA