What type of tenancy is this?

Tenancy Types and Management

I have a letter signed by me as the only piece of paper that exchanged hands. Its copied below. Is this a "implied assured shorthold tenancy". My tenants are on DSS but have not paid over any rents for two months. Plus they are damaging the property and I really need a repossession. I need to use accelerated possession order but am doubtful if I qualify due to typoe of tenancy and that I have not deposited the deposit in any scheme as I thoughjt this is not an assured shorthold tenancy. Any advise on quick fix for possession?

Nasser
copy of the only tenancy letter issued and tenants have not signed anything:

"In accordance with the terms of our agreement, I am writing to confirm your status as a tenant renting Three Bedroom self contained Flat at the above address from 4th of June 2009. It includes free residents parking for your car.

Your rent is £1150 per month excluding all bills except for building management service charges and house insurance. You are also required to place £1650 returnable Bond/Deposit for this arrangement and I confirm that this has been received.

Any rent arrears is payable as soon as you have received Housing benefits and must banked/paid regularly afterwards. The property is let as unfurnished with minimum term for six months after which, one notice period is required from either side. The rent is reviewable every year."