I depends what Jurisdiction you are in (Scotland, Northern Ireland or England & Wales). typically, most legislation requires a lease (stating price, length of tenancy, subjects, and the parties) second a 'notice to quit'. in terms of home improvements, you can counterclaim for improving the enjoyment of the property which while you enjoyed, inevitably the landlord (Property Owner) will enjoy far more over the period of the property is rented to you and others in the future.
Exactly what is the reason for Section 21 request for 'Notice to Quit' as there is many reasons i think between 7-17.
In Scotland (which is where I am with my Two Law degrees), it can take 6 months before a court can hear a case, furthermore, set dates for evidential hearings etc.
If it is family members that are renting to you, is there anyway to repair the relationship for renting?
Furthermore, if there is an arbitration clause in the lease agreement (in Scotland) it is mandatory to enforce this before going to court (not sure in England & Wales). England & Wales may have a legislative section in the Arbitration Act 1996 about applying to the court for stay of proceeding while seeking arbitration (not too confident, but it would be a logical guess).