I want to be positive and encouraging to you, so that you can all have a really nice time.
I'm afraid I am being all negative, which I don't want to do.
If you are staying in or near Mickleton which is just outside Chipping Campden I agree that you will most definitely benefit from having a car and a good GPS, and a navigator who can tell you that the GPS is pulling your leg when it suggests to take a dirt farm lane to approach Mickleton from the Fosse Way. Unless you all have very small carry on luggage only, and none of you are large, you want to be sure your car is big enough, and has a big enough boot.
But - if you still think that driving as a rookie is ok in Central London on a Monday morning I need to warn you of several concerns.
The car rental place gets uniformly awful reviews on Google and Google +. It closes at 4 on a Sunday, if it were me I'd want to get there plenty early if I wanted a choice of cars or an automatic or other special requirement. I'd take lots of photos when I hired the car. I'm not clear on when your trip is, but if it is anytime soon, it will be getting dark as 4pm arrives.
Check really, really carefully before you park the car for any CPZ (Controlled Parking Zone) signs, exactly what the restriction is - it can change part way down the block - and can be different on each side of the road. Check for any road markings, any signs near the space, and most importantly for any red or yellow lines on the road. Parking offences are expensive.
Is your hotel inside or outside the Congestion Zone? If you trigger the cameras for the Zone you have to pay the very expensive cost immediately or it gets much higher than that.
There isn't a really good driving route from Central London to Canterbury. Maybe the A2 once you get clear of London, but the problem will be crossing the river. None of the bridges in the centre of London lead onto a particularly fast, convenient or easy route. Staying north until the Blackwall Tunnel or Woolwich Ferry is very slow, congested, and then the built up part of the A2 which is very slow.
You could go east from the Isle of Dogs to the M25, then over the Queen Elizabeth II Bridge but then that is very slow and crossing at rush hour is almost guaranteed to give heartburn and you have to pay the toll electronically because no tolls are collected at the bridge but all cars are photographed. Failure to pay is very expensive.
Parking in Canterbury, my experience, is very difficult.
Then you have to do it all over again from Canterbury to Chipping Campden. You have to use the M25, and you have to use about half of it no matter which way round you go.
If you go anti-clockwise around from the A2 you have the problem of crossing the Thames Estuary almost immediately but the QEII Bridge is only clockwise so you will have to use the perennially backed up and crowded, very narrow, complete with chicane to enter Dartford Tunnel. Like the bridge the toll has to be paid electronically right away or fines get very high very quickly. Then just about half way around the notorious M25. Don't count on any map to give you a true transit time because of construction zones which have very strictly enforced yellow speed averaging cameras at which they will send you a ticket for only a very small breech of the 50 mph limit. There are also gantries on the non construction areas where cameras enforce any posted speed displayed on the gantry. Don't try to do the national speed limit unless the gantries are dark or showing the national speed limit sign.
Once you get off at the M40 the run should improve.
Or, you can choose to go clockwise around the M25. Good idea, no tolls, but then you almost always run into the awful traffic around the M23, Junction 8, Junction 9, the M3, the A3, the M4, all around Heathrow including Staines and the A20, and then onto the M40.
Neither way on a Monday will be a walk in the park.