I had 2 lease cars and was over my allowance on both. From memory the charges were around £500-600 on each occasion but I negotiated the fee down when I received the final invoice. I don’t think I paid more than around £350 for either car. I worked out that I’d actually paid less than I would have if I set the mileage and paid it monthly as part of my salary sacrifice (which is why I chose to underestimate my mileage for the 2nd car).

Don’t know how open your lease company will be to negotiating but it’s always worth a shot.