Alice rents a house to Bob under an assured Shorthold Tenancy and the fixed term expires. Alice now wants Bob out, so she must serve him a s21 notice of two months Bob has an option to not leave after this period in which case Alice can go to court and pay a £355 fee to apply for a possession order.
Would it be blackmail or otherwise illegal in any way for Bob, toward the end of this period, to say to Alice in one way or another, "look, I don't really want to leave, but I am entitled to stay here until you get an eviction order that could take about another month at the absolute minimum, and it will cost you by the end of the day £355+£155=£510, at no adverse legal effect to me.
Why don't you give me £400 toward a deposit on my next place and I'll sign a note of surrender date with an effective date in two weeks time?