IANAL however.... Your daily storage rate is way too low. It will cost you more to get what they owe you than you will get out of them.
Send them a letter changing the rate to £250 a day and stating payment terms of 30 days.
You have to be (legally) reasonable, so give them 14 or 28 days to get something sorted, after which the new rate will apply.
You should send them (snail mail and email) invoices every week reminding them of their ongoing commitment to paying you.
They may not pay you, in which case you have to go through small claims (Google it) or sue them to get the money they agreed to pay you (by not removing the vehicle after you gave them a reasonable time to comply) the former costs you time and effort the latter cost time effort and money.
In my experience, once invoices for significant sums start adding up to being a PITA for them, things will happen. Once the car is gone you have to decide if it is worth your time and effort to chase down the invoices. Hint - it probably isn't.
I got rid of incompetent bailiff companies this way (they kept buying a debt that someone had taken out using my address as theirs and the original loan company didn't check)
tl;dr - you have to make it worth their while to make you go away whilst being cool, collected and, above all, reasonable.