I assume that the tenancy was an assured shorthold tenancy (it will be unless you served a notice on the tenants at the start of the tenancy stating that it was not to be an AST). The tenants are now occupying the property under a statutory periodic tenanct.
Firstly you cannot change the locks; they have a right to occupy the property until the tenancy is terminated.
As the term of the tenancy has expired you can serve a s21 Housing Act 1988 notice on the tenants (both are still technically tenants) requiring possession of the property. You must give two months notice of this and the notice must expire on the last day of a tenancy period (eg. last day of the month).
Your second option is to serve a notice stating one of the permitted grounds. If the tenant is two months in arrears of rent (and the rent is payable monthly) then you can serve a s21 Ground 8 Housing Act 1988 notice requiring possesion. If they are not two month in arrears then you can serve a s21 Ground 11 Housing Act 1988 notice on them for persistently paying rent late (if they have done so). The period for these notice is only two weeks so it is a lot quicker than the notice in the paragraph above.
It is very important that the notice you serve is in the correct form, otherwise you will have to start the process again. You can download notice from www.lawdepot.co.uk/contracts/eviction-notice-forms
If the notice period expires and the tenants have still not left then you will have to make an application to Court for an Order for possession.
In order to recover the outstanding arrers after they have vacated you should intially write a letter before action to her with respect to the outstanding rent. State the money outstanding to her, refer to your tenancy agreement and ask that she pay the amount outstanding within a reasonable time (eg. 14 days).
If this does not result in her pay the outstanding rent arrears to you then You can recover the money owed in arrears of rent yourself by using HMCS's online service www.moneyclaim.gov.uk
It's pretty cheap and very straightforward to use.
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