Unsure how far you require transport but check out "Amari Supercars" Preston.

They have a dedicated covered trailer for transporting vehicles and offer this service I am sure.

I have used Ron Hodgson specialist cars of upholland twice. Not sure if they have a coved transport but have been very pleased with their service. They delivered my 1942 jeep down to Oxford and the also colected my Ariel Atom from Somerset. They are good with the price also