EC261 does not cover consequential loss. Nor does the Montreal Convention. You will need to meet any additional costs from your own pocket - unlike the advice given above, I’d say it’s extremely unlikely travel insurance will have clauses to cover these specifically, unless you have a very, very good policy.
It’s certainly correct to say, with a mechanical defect, you’ll get 600 Euros per person delay compensation. Wait a week or so after you get back to allow the flight to be noted as eligible in BA’s system and put the claim in - you can submit it on BA’s website.
It would be worth you explaining the reason for your extended stay when you reach the car park - it’s not unknown, but equally not guaranteed, for the operator to write-off some or all of the excess charge.