Take a plane ... GBP 243 for you and your family return ticket with Wizzair from for example Luton to Katowice, then rent a car with for example express.pl for 18 or 25 E a day with free mileage. No hassle with your own car and probably all in all cheaper as well. You can even rent a local satnav.
Don't forget, you'll be using about 350 litres of fuel if driving from London (GBP1,20 in UK, E1,48 in B, E1,58 in NL and E1,40 in D), so it's actually a lot cheaper. And with the harsh winter we've had throughout Europe, you can expect hundreds of potholes (okay, not on the motorway) which can seriously damage your car.