Bed Bugs in single occupancy

Other

On Friday, the tenants of my single-occupancy flat reported bed bugs. It seems these bugs had been noticed by them a few days earlier.

I called in a pest controller who sprayed a treatment over the weekend. Unhappily, such treatments are not immediately successful so there will be a period before the bugs die off.

Reading the check out report for the previous tenants and the check in report for the new tenants, I found no mention of bed bugs. I am pretty sure these bugs have been brought into the flat since the new tenants arrived.

The tenant is asking for replacement beds and mattresses, which is an expensive option. 

As it seems the bugs arrived after the tenants took over the flat nearly 3 months ago, I feel that they should bear the cost of replacing the bed and the early replacement of the mattress.

Am I being reasonable and what is the legal situation here? The 2-bedroomed flat is occupied by one family

All advice welcomed. 

Thanks,