HI thanks for your question. My name is ***** ***** I can answer this for you.
If you have a valid s.21 notice served on you, then you should leave by the date in that notice, otherwise, the landlord can issue Court proceedings against you to seek possession. However, he cannot remove you unless and until the Court makes a possession order.
You can obviously look anywhere you like for a new place, and you can leave at any time, but you're still liable for the rent on the existing premises until the date of your tenancy expiring.
I am ready to pay the rent until I find a suitable place but if I do not find a suitable place in time can I stay a month or two till I find one. How long does it take to get a court order and will it cost me.
It will probably take him about 5/6 weeks to get the Court order, and you;d have to pay the rent for this time and the court costs (probably about £300).