If the tenancies are periodic tenancies then you may serve a s21 notice under the Housing Act giving them 2 months notice with such notice to expire on the final day of a rent period. He does not need to give a reason for this. After the notices have expired he may then apply for a Court order for possession if the tenants did not vacate. It's very important that the notice is in the correct form and served correctly, there are a number of online document providers who you can google in this regard.
There is nothing illegal about offering the new tenancy with deposit but stating that if this is not accepted then he will serve the s21 notice period and issue possession proceedings if they do not vacate. It's hard bargaining, it's not illegally - it's the landlord's prerogative on what terms he is to offer.
Remember, of course that any deposit taken will have to placed in a tenancy deposit scheme:-
If the deposit is not so placed then the tenant may be able to sue you for the return of the deposit and a fine payable by the landlord to him of three times the deposit amount..
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