Tenancy agreement only signed by tenant

I am a non-resident landlord. The agent currently acting on my behalf is not the agent I originally signed up with (company was taken over last year). Recently they found me new tenants, but they never provided me with a copy of the tenancy agreement. After chasing it I discovered it only had the signature of the tenants – the agent had not signed it on my behalf. 

When questioned, the agent said it is not their policy to sign tenancy agreements – however they did not tell me this until now and I am worried that without my signature the document is not legally binding. My agent says it only needs the tenants signature, however I thought both parties had to sign it? Wouldn’t the tenant need a signed copy?

Also – on a separate issue, the new agent is arguing that the conditions agreed with my previous agent is not covered under the service they provided – i.e. I had agreed property inspections twice a year but the new agent is saying inspections with them are additional extras not covered under their standard management service. I have already argued the point that I have not agreed/signed to any new terms so as far as I am concerned my current terms still stands and they have reluctantly agreed, however I have yet to see if they carry out the inspections.

Am I in the right?

Any advice much appreciated.

Regards

Tania