It depends on what damage the excess is to cover. If the leak caused damage to a communal area, it is likely that an insurance claim would have been made by your landlord to repair the damage as quickly as possible. Their insurance company may then try to recover the money from the owner and if they are successful, you should get the excess back (but your management company/landlord will probably take a fee for sorting it all out so you probably won't get all of it back).
Any expense incurred by you to cover the damage to your flat should be claimed from the owner directly although again, you may want your insurers to pay you now and try to recover the money from the owner later. If they are uninsured losses and the owner refuses to pay, you may have to go to the small claims court to get the money back.