The solution to this problem, that would be easy to administer, and would not only be self financing, and vote winner and make a few million quid a year for the exchequer would be to do what the Swiss have done for years.
Ensure that all vehicles entering the country have a "Road Tax" disc valid for the length of their stay, The Swiss ones are valid for one month, and cost about £20 from memory, you can buy them valid up to one year.
If you pay by credit/debit card than any parking tickets/speeding tickets you clock up in your time in the country are automaticaly deducted.
If you pay by cash then you have your passport copied and address details taken
Given that we are an island and there are only about a dozen vehicle entry points this would be very easy to administer as you sell the 'tax disk' on the ships or at the Eurostar station.
Any vehicle trying to leave the country without a valid disk would be caught by the Vehicle ID cameras that are already in place at every port to spot stolen vehicles.
Stikes me as being a win win situation for everyone except those trying to flout the rules.
It would also go some way toward paying for the damage caused to our roads by foreign registered HGV's