You will be on a rolling contract then (if you do not sign a new contract every 6 months/year, then your fixed term contract converts to a periodic (rolling) tenancy), so 2 months notice is the legal requirement. He isn't obligated to have the boiler serviced, but he is required to have a gas safety certificate issued every year covering all gas appliances. However if he hasn't done this, it will have no effect on the section 21.
I understand you don't want to move, but unless he agrees to an extension then there is nothing you can do.
We tried selling a tenanted property and it was so difficult that we took it off the market. Mortgage companies sometimes have problems with tenants being in situ as well, so your landlord probably thinks having an empty property is the best way to sell it.
Hope the council can help you and that you get a new a home you're happy in x