good luck, TV reception is not good in car let alone Digital TV.
you will have to re-tune it every 5 mins of driving to allow for distortion in the signal, reflection from buildings whilst also rotating the aerial for the best signal, you will also need a powered amplifyer, and a wide band aerial, you can get portable one but they are £30 for ones that work, and a decent power supply, thats smooth.
btw i wouldnt want to watch big brother or east enders whilst driving anyway ..this would be for at shows ect so i would be parked up and also the football at work
Provided you stay in range of the same transmitter you won't need to retune the box, but i'd check you have a good reception first here: http://www.dtg.org.uk/retailer/coverage.html
Freeview reception is gonna be flaky until analogue gets switched off (between 2008 and 2012 - that link will also tell you when your switchover date is) because the band is very crowded.
I agree Dusk, borrow a freeview box and test your reception though