Guys, shouting and balling and contacting every magazine and TV show in the country will achieve NOTHING. All its likely to do is limit your options with the supplying dealer.
Take some advice from someone who HAS rejected a car, write to the dealer manager/principal or sales director.
List your reason for rejection, visits made for items to be rectified and the results etc. Listing your last 10p of fuel and bus fare just puts their backs up.
Your ideal result is to have use of this car or another until a replacement arrives. Calmness and firmness is the key here. Its the dealership who will have to find a replacement car, at their cost. If they feel you want every last penny of expenses then they could well just refund your money minus fair wear n tear charges, and that position could lead you to court to find a better solution for you. Certainly contact customer services to inform them that you are rejecting the car in writing with your supplying dealer - they may offer to asisst in finding a quicker rebuild slot, dependent upon the dealers reaction.
VWUK are only responsible for allocating cars to their franchises and ensuring they represent the brand - if the dealer fails to achieve the VW level of satisfaction then VW simply drop them. VW may asisst in resolving the matter speedily , but thats all.
Timescales - it took me 2 weeks to get the money back, but that was on a car i left in the showroom with delivery miles, and the 2 weeks was down more to me signing to say i wasn't the first owner so they could remove my name from the V5 and claim the car to be new. It resold within days of them having it back on stock !
You could be looking at 4 weeks of polite negotiation - stress you have no confidence in the car and want a quick solution.
Until you get their initial response to your rejection its complete speculation what your next move is .
Good luck.