Can someone explain the process, details below

I’ve issued a section 21 to my tenant as I am going to sell it after some renovations. I downloaded the form online and filled it out with some guidance online and noted 1st of November as the end of the tenancy. Giving 1 week more than required legally.

Few quick fire clarifying questions…

What happens next? I do not think the tenant will leave themselves as they’ve hinted. Will I have to get a lawyer and go to court?
How long does this usually take from everyone experience?
Will the tenant have it on their record that didnt leave or does that happen if they dont leave after the court says to do so.

I think their plan is to go to the council and get into social housing. For which they need to be “homeless” to speed things up. But this is just me guessing i dont have proper evidence for this.

Thank you

If your tenant does not vacate, send an email,if this is how you usually communicate, explaining that as they have not left the property you will be soon commencing proceedings through the court to regain possession of your property. The cost of which, the tenant will ultimately have to pay for. Also let them know that they are still liable for the monthly rent and all other obligations as per the tenancy agreement. Let them know the waiting list for social housing are years long and most people end up being placed in emergency accommodation.
Should they decide to stop paying rent, inform the council immediately, as this is seen as making themselves voluntarily homeless.and begin Section 8 proceedings once they have missed 2 payments. If you are not confident of the procedures seek professional advice from a specialist housing solicitor.
Be aware that many tenants can gain lots of information from various Facebook groups etc, specifically formed in order to share ,and try, every trick in the book to make things as difficult as possible for Landlords.