genie if you have previously had a Tenancy Agreement, once that agreement comes to an end, and you have not had an eviction notice, your Tenancy rolls over onto a monthy lease until your landlord offers you a new Lease. Therefore if you are still paying rent you are legally allowed to live in your home.
The Estate Agent was wrong to backdate a Tenancy Agreement. Contact the Agent directly, explain you have yet to sign the Agreement as it had discrepencies, and ask for a new copy to be sent. Follow this up with a letter sent recorded post.
It make take a few weeks to sort out, but as long as you continue to pay your rent, you are 100% legally living in your home and your rights under the Shorthold Tenancy Laws are unaffected.