Once your fixed term comes to an end your tenancy will usually move automatically to a monthly rolling contract which is called a Statutory Periodic Tenancy, unless your contract says otherwise. The rolling contract is the default if your contract is silent on the issue.
Generally, the landlord cannot evict you until after the end of your fixed term. Thereafter he can evict you any time by serving you 2 months notice (at the moment it is 3 months under emergency coronavirus legislation).
If your landlord wants you to leave at the end of your fixed term then he has to serve you the notice 2/3 months before the end.
In terms of renegotiation, you are entitled to do so although most landlords will be unwilling to negotiate, especially as the rental market is actually quite strong.
If they agree to renegotiate they might ask that you sign up to a new 6 or 12 month term. They are allowed to do so butt of course it's up to you whether you agree.
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