Insurance claim for water leak

Other

Hi, I have bought a flat which I have been renovating as a buy to let . There was a leak from the upstairs flat causing considerable damage to mine which is the one below .
The freeholder has an insurance policy to cover this but I have now found there is a %C2£500 excess on this . The cost of my repair was %C2£1100 which I have had to pay to urgently fix the leak . The invoice for the damage made out to the above landlord stated there were 5 leaks to be repaired and the insurance are saying 5 leaks will be 5x%C2£500 excess which means I will get nothing . I have however highlighted that only one leak caused the damage to my flat and submitted evidence to prove this so hopefully I will just pay 1 excess and receive %C2£600 towards the repairs.
Is there anyway I can get the upstairs landlord to pay the excess as his repair bill is outstanding and so I can't add to his claim . It seems wrong that I am paying the excess for his negligence . Please can you advise me of steps to take to claim this money from him ?
Thank you ..... Jane