The law regarding traveling with dogs has recently changed
Driving a car with an unrestrained dog, can invalidate your insurance and lead to fines of up to £5,000
The Highway Code Rule 57. When in a vehicle make sure dogs or other animals are suitably restrained so they cannot distract you while you are driving or injure you, or themselves, if you stop quickly. A seat belt harness, pet carrier, dog cage or dog guard are ways of restraining animals in cars.