S8 and S21

Possession - Section 8 and Section 21

The tenant has failed to remove another family he has allowed to stay since at least August 2023 since it became known.  He was issued with a warning to state section 8 will be issued if the extra family he is allowing to stay has not gone by the 1st December.  Today, 1st Dec the tenant has asked if they can stay until the 22nd December. However, he has constantly given reasons since August of them moving out and for reasons/excuses does not happend.  I nolonger trust him.  But I am also worried that if I issue section 8 - the courts will take a long time that it is not worth it.  His tenancy agreement should finish in June 2024 which i would like to bring forward as he has ruined the property as well.   
Pls advise if it is worth issuing Section 8 or 21 or both. or what I can do safety and within reason.  The damage is mainly of damp that having another family of four staying in one room has caused.  Thank you all.  I am getting very stressed out over this and trying not to worry for my health sack.