hi salsapriestess, welcome to the Forums
I don't want to discourage you, but I don't know your driving experience in England.
Are you aware of the driving conditions in February? Sunrise in Canterbury on the 6th of February will be at 7:25 and sunset at 4:54 pm, which sounds pretty good, but you should expect your headlights to be on probably at least 2 hours after sunrise and 2 or 3 hours before sunset because the sun is so low in the sky, and actually seeing the sun is so unlikely in February.
Also expect the roads to be continually wet, even if it hasn't rained for a few days - the sun is far too weak to dry the roads - so expect glare from oncoming headlights and from the road itself. That is also prime pothole creation time after the road has frozen and thawed and cracks open up - after years of austerity the roads are quite full of potholes, so if there is a puddle don't drive into it.
Where will you get the car after London? You're not planning to get it on landing and driving into London to park it for 2 days?
Since you are only spending two days (including arrival day?) in London can we assume that you have been here before? If so, welcome back!