Where to visit between London and Canterbury

I would recommend Whitstable on the coast- a very nice place to stay, good food options (known for oysters), and you can get there on the fast train from St Pancras. From Whitstable it's easy to get a bus to Canterbury.

Other nice places roughly between London and Canterbury: Knole, Chartwell, Leeds Castle, and (a bit further afield) Sissinghurst Castle Garden.

Now I've read the tour itinery, I see you mean you meet up in Canterbury late afternoon and the cathedral is included next day. By arrive in London I'll assume you mean Heathrow, probably mid morning.

The first thing that comes to mind for me is the perennial problem of luggage, it might be worth you booking a room at the tour hotel, go straight there to leave luggage and then set about seeing some sights. From Canterbury on the 27th and assuming you are a little jet lagged, you've dropped your luggage and by now it's early afternoon take a local bus to Whitstable and get some sea air. And oysters!

28th train to Chatham and see the Historic Dockyard https://thedockyard.co.uk/

Also, just next to Chatham is Rochester - the 2nd oldest Cathedral in the UK, a pretty good Castle and the shadows of Charles Dickens everywhere you look.

Thanks for the suggestions. Any recommendations of where to stay in Rochester?

If I was looking to stay in Rochester my first choice would be the Golden Lion- a Wetherspoons Hotel- by some way a more upmarket budget chain than the likes of Premier Inn- always in nicely converted old buildings.
You can only book on their own website.

Interestingly any time I've looked Rochester is more expensive than their property in Canterbury - which surprises me a lot given how Canterbury is tourist central.

I'm staying at a Wetherspoons in Wales tonight. Unlike any normal budget hotel I've been looking forward to the stay for weeks, and it hasn't dissapointed.

I was in Rochester a few days ago, the hotel has an excellent location on the High Street.