If are unfortunate enough to have suffered damage to your property, whether by a leak, fire, frost or weather damage, it is likely that your buildings insurance will cover the damage (less any excess).
For leaks, the insurer will normally pay for trace and access, but not fixing the actual source of the leak. However, damage caused by the leak is normally covered.
Whilst the insurer may try to push their preferred supplier on you, you do not have to use them.
From personal experience, I have found the insurers' contractors can be very useful for the initial boarding up trace and access etc, especially out of hours. However, because they believe they are guaranteed to get the work, what follows is often not great service.
Trying to get an appointment that suits you is difficult. Then, because they want to keep the insurer happy they often under specify the work.
For example, following a break in, my front door was kicked down. This broke the door and the door frame, which also ripped away from the stud walling and caused a large crack in the plaster and moved the stud work.
The insurer's contractor sent an estimator who could only deal with fixing the frame and fitting a new door. Next we received calls trying to book that work in. Even though they had not drawn up the correct specification and their work would all be undone when the walls are repaired.
Luckily you don't have to use the insurer's preferred contractor.
Get two quotes yourself from contractors you trust. The insurance company might want an assessor to check that the work needs doing, but that is it.
You get work done by people you trust and time that suit you.