Here is the scenario. You have served a four-month Section 8 notice on Ground 1A because you want to sell. Two weeks later your tenant says they have found somewhere and will be out by the end of next month. No court, no bailiff, no argument. Then the sale falls through — or you change your mind — and you think: the tenant left voluntarily, there was never a possession order, so surely the re-letting restriction does not apply to me?
This is deliberate drafting. If the restriction only bit when a court made an order, the obvious workaround would be to serve a Ground 1A notice, pressure the tenant into leaving "voluntarily", and then re-let at a higher rent with no consequences. That is precisely the behaviour the restriction exists to stop. Tying it to service closes the loophole.
So the sequence to hold in your head is: notice served → restricted period begins → runs until 12 months after the earliest possession date stated in the notice. Roughly 16 months in total. Nothing the tenant does shortens it.
Offering a tenant money to leave is not unlawful in itself, and a clean negotiated exit is often better for everyone than four months of notice followed by a court queue. But two things go wrong repeatedly:
Get it in writing, dated, signed by every joint tenant, stating the date they will give up possession and that the tenancy ends on that date. Deal with the deposit and any arrears in the same document. Take meter readings and photographs on the day the keys come back. An informal "they said they'd go" is how landlords end up with a tenancy that legally still exists and a new occupier they cannot evict.
If there is more than one tenant on the agreement, note that the rules on joint tenancies matter here too — a surrender needs all of them.

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Take the free compliance check →Ground 1A and the 12-month re-letting ban · One sharer leaves: joint tenancies · You've got a possession order — what next?