Can I just not renew their contract and go back to my place in 2 months or do I still need to give them 6 months' notice?
6 months' notice
I'm assuming this is a fixed-term Assured Shorthold Tenancy.
Unless a landlord is going down the Section 8 route where the tenant has broken the tenancy agreement, they will need to serve a "Section 21 Notice" under the Housing Act 1988 requesting the tenant to leave a property.
The Act has been amended to extend this notice period to 6 months, and any fixed-term tenancy that ends during that period will roll over to a periodic tenancy until the end of the notice period.
This is the relevant extract from the government's website:
Section 21 notices requiring possession of a property under an assured shorthold tenancy
Landlords can only use a Section 21 notice to ask their tenants to leave their property:
If the notice expires at or after the end of the fixed term.
During a tenancy with no fixed end date - known as a ‘periodic’ tenancy.
From 29 August 2020, a Section 21 notice must give tenants at least 6 months’ notice of the fact that the landlord requires possession.
This give some more detail about s.21 Notices.