The simple and fair answer would be no. Head of the ARLA Propertymark Legal Helpline gives reasons here;
“The answer may be “no”. There is a concept in English law which suggests that if a landlord does something – for example serves a notice – and the tenant relies on that to his detriment, then the landlord cannot change his position. The principle is called estoppel.
“It could apply where a tenant received a 6 month notice, made arrangements to view other properties appropriate to that Notice and incurred expenses as a result. If a second Section 21 notice expired before the original 6 month deadline, a tenant could argue that the second notice was effectively invalid.
“Please make sure landlords are aware of the potential risk before serving a second Section 21 Notice if an earlier Notice is still current.”
To be fair to tenants, existing notice periods should be honoured.