IMHO, the tenant is probably not legally required to move out at all, as matters currently stand.
If you want to regain possession, then it is probably up to you to serve a notice on the tenant under the Housing Act, to terminate the tenancy. This would be the prudent course of action.
Certainly the surest way to get rid of this tenant is for you to simply give the statutory eviction notice. Read this thread on how to do it:
http://www.consumeractiongroup.co.uk...-eviction.html
As to Surrender -
There has probably not been a surrender, because (a) the tenant has not vacated the premises, and (b) no deed of surrender has been signed.
The most there can have been is an agreement to surrender at a future date. But as there is no deed, an agreement to surrender might not have been validly formed, legally speaking. Did money change hands? If not, there is probably no valid contract of surrender, because payment of money (known legally as "the consideration") is
necessary to make a contract legally binding, except where the contract is in writing and under seal (i.e. where it is embodied in a deed).
You might argue that there was valid consideration, since you changed your position, legally speaking, by agreeing to re-let (if that actually happened). But you will certainly need to engage a solicitor to argue the complex legal issues that would then arise.
Moreover, if there is nothing in writing to prove the surrender, it is your word against the tenant's as to whether the surrender was actually agreed, or was still being negotiated.
There is no part performance here that might evidence such a contract, because the tenant has not vacated the premises.
But the common law rules are very complicated, and you might have a futile time trying to argue them in court, where anything can go wrong. And a Court action might taken several months.
As to the tenant's notice -
It is certainly not possible to terminate a fixed term tenancy by notice, so the notice given cannot have done that (provided that the tenancy agreement does not contain a "break" clause, also called a notice clause, allowing that: which I assume it does not, as you haven't mentioned one).
It is probably not possible to terminate a tenancy which does not exist. If so the notice given on 7 October can't have terminated a periodic tenancy that has not arisen (the fixed term not yet having expired). A tenant must give a minimum of 28 days notice to terminate a periodic tenancy, but your tenant probably cannot do so today, or on 7 October, since no such tenancy existed at that date.
But the common law rules are very complicated, and you might have a futile time trying to argue them in court, where anything can go wrong. And a Court action might taken several months to be heard.
Advice & opinions on this forum are offered informally, without any assumption of liability. Use your own judgment. Seek advice of a qualified and insured professional if you have any doubts.