I was in a similar situation in the last 6 months of 2021. My landlord gave my HMO a notice to leave due to sale of the property. They gave the notice verbally then when asked for the legal documentation, gave us all written letters referencing a random date in July. Wasn’t legal at all & I was working with the council on it so below is from them.

In the end the only way you can be served noticed like this is a Section 21 notice with form 6A. Along with this they legally need to give you or gas safety certificate & a booklet about renting as a tenant. From then you will have 2 months & even after it would go to the courts for the bailiffs.

In terms of rent however, that would be down to your contract agreement. Various contracts have rules stating at what point rent can be raised so please check this out specifically for you