Can I change the locks if tenant stays on despite ending periodic tenancy?

General Discussion

We have been renting to a same sex couple (with children) who are married.  They have been renting with us for 7 years and the tenancy is periodic.  The relationship has now broken down and one has moved out and advised she wishes the tenancy to end which it is due to do on Monday next week. The remaining tenant has indicated she wants to stay on.  We agreed she could stay but she is now proving to be elusive.  We need a new tenancy signed by her which she requested and which is due to start on Tuesday.  She has now gone radio silent, ignoring calls and texts.  We now suspect she may be planning to stay on in the hope we will evict her so she can get a council property.

As the tenancy has been ended by one of the parties I believe it ends for both.  Due to this, can we go round and change the locks on Tuesday despite one of the tenants not moving out?  Or, do we have to go down the route of possession and eviction?

We have always had a good relationship with these tenants and cannot understand why the remaining one is ignoring us, particularly when she was so desperate to stay.  We now want her out asap but need to know the legalities.  I have seen online that she would be effectively trespassing and we can change the locks but I have also read that we need to go to court and serve eviction - despite the tenancy being ended by the other tenant! If this is the case, we want the quickest eviction route possible.

Any advice would be appreciated.  Many thanks.