Keza
Your partner needs to take this up with Esure. If they are cancelling the policy, they have to confirm this in writing and give a minimum of 7 days, so that the policyholder has a chance to resolve matters.
Normally Insurers will issue a couple of letters regarding the payments, before they threaten cancellation. If your partner phones Esure customers services he will find out.
If you want to make sure they Insurance is kept in force, you could always make the payment for him. He would have to phone them and then hand the phone over to you. Esures accounts team should be able to accept a card payment to replace one of the Instalments. Once this is done, Esure can then provide confirmation of cover, to give to the police.
Huckster