Accident in hire car. How liable am I? (England)

So a few days ago I hired a car for a day trip. Unfortunately I struck a pothole resulting in two tyres being blown.

I was able to pull over and contacted the hire company - they advised they would contact their roadside assistance contractors who would then come out to me.

After about an hour of waiting, the company called to say they would be unable to offer roadside assistance as they couldn’t source the correct replacement tires for the car. They said the vehicle would need to be towed, and that I would need to abandon the vehicle (in the pub car park where I pulled over), and that I would need to make my own arrangements for the onward journey from that point (costs for which they were happy to reimburse).

They have sent information via email stating that once they have inspected the vehicle and any damages, I may be liable for costs including both repair and the transport/towing of the damaged car.

I realise I may be at fault here - and would expect to pay for the replacement tires.

My concern is that I will also have to pay the towing fee needed to recover the vehicle which is likely to be very expensive. My point of contention against any charge here would be that a hire company should have the mechanisms in place for what is a common and simple roadside repair such as a replacement tyre. In not doing so are they fulfilling their obligations as a service provider, and is it fair or reasonable to expect a customer to have to pay for a potential shortfall in their roadside assistance provision.

At this point the company haven’t completed their inspection so I can’t say for certain what charges I’ll face.

Thank you for reading!