Advice needed

Rent Arrears

I have a tenant who holds a six month AST and has been in the house for 2 year. Everthying was fine but lately she has amounted arrears running to about £1100 due to chnage in hosuing benefit (bedroom tax). Council has agreed to pay me HB direct but this leaves a shortfall of £40/week which I know will be difficult in getting from the tenant. My question is this do I serve notice and proceed on the basis that AST has expired and I want reposssion and arreas also means I want paying or do i serve noitce just on graounds of arreas in the hope I will be granted posssion. My feeling is former is easier in that I don't have to give a reason. What recall do I have if she becomes diffcult and damages my house?

thanks