If you have insurance, then pass this to your insurance company.
The GBP2000 for repairs is straightforward enough because presumably there will be receipts and quotations for that.
The landlord is going to have to prove that the property was uninhabitable (and not simply that it was empty because it could have been empty anyway and the landlord could be trying to recoup rent which hadn’t been lost!).
So what would be important is that the was a tenant in the property and the tenant had to move out.
From the leak that you describe, the damage on its own seems to be remarkably high unless of course you were, for example, on holiday and this happened for a fortnight.
If you want to deal with it yourself, rather than pass it through your insurance company, then I would ask for a complete breakdown of what’s being claimed.
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