No, the landlord has himself in a pickle.
If your previously tenancy has expired then you are occupying the property under a statutory periodic tenancy which means that it continues on the same terms (inc. rent) as the previous tenancy but from one rent period to the next. In these circumstances the landlord still has to serve a valid section 21 Housing Act 1988 notice upon you giving you two months notice with such notice expiring on the last day of a rent period.
The notice he has served you is invalid and a Court will not make an order for possession on it.
He would have reserve the notice in the appropriate form and wait until it expires before making an application to Court for an order for possession so that you would have to leave.
If you wish to vacate the property then you would have to give only one month's notice if the rent is paid monthly, it must be in writing and it must bring the tenancy to an end at the end of a full rent period. You should serve this accordingly to marry your vacation of the property with your new accommodation.
You do not have to pay increased rent and are not yet under an obligation to leave the property. The landlord does not know what he is doing.
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Thanks for that Thomas,
Could you tell me if a landlord wishes to increase the rent, does he have to give a certain period of notice?
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