According to my route planner it's 291 miles from Birkenhead to Dover over some of the worst roads in U.K. M6-M1-M25. That's 600 miles round trip including miles in France. Cost at 40 mpg = £90. Ferry, say,£35. Are you going to do it in one day? If not, hotel, say £40.
Cobby is right; there's not so much saving to be had these days, also, remember that a lot of wine that nobody wants to buy ends up in those places.
About ten years ago, I used to go a couple of times a year on business, so the firm covered my costs and I used to buy some wine and since I was a smoker at the time, a couple of thousand cigarettes which were a lot cheaper then; I'm not sure they are now.
If you're still determined, here's a link:http://www.calais-guide.co.uk/wine-and-beer-outlets.html