The company we used has been sold, so I can't make a recommendation, but what we did was have them drive us to Canterbury and leave us there for a few hours, sans luggage. Then meet us a fixed time and drive us to Heathrow. It worked out very nicely, we had lots of time to see the cathedral, stroll around town, do some shopping and have lunch.

Wendy
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Booked: Uniworld Egypt, 2015
Tauck Amsterdam to Budapest, 2016
Paul Gauguin, Societies & Tuamotus 2016