I'm visiting Kent county in August for a quick 3 day visit. Staying in Chatham one night, then moving to Canterbury area for the second night, departing for France via train from Ashford. I have booked the trains and planes that will get me to and from England, but haven't booked the Chatham to Canterbury nor the Canterbury to Ashford sections. Would I be safe to book these once I'm in England (ie do the trains and buses sell out quickly at this time of the year?).
Ah, lovely Kent (you don't have to put county), used to live in Chatham when I was a lot younger. The main advantage to buying advance tickets is that it's usually cheaper than walk up fares but I'm guessing that because these journeys are fairly short, the walk up fares will be the same price (perhaps someone with more knowledge can confirm).
There's no need to buy advance fares for those short journeys. You won't get much discount, if any, and hardly any British trains ever "sell out".
Kent has lots of railway lines, all with frequent service (at least one train per hour).
You don't need to "book" tickets in the sense of reserve a place on a specific train. For these short distances (Chatham to Canterbury to Ashford), just turn up at the station, buy a ticket and get on the next train. On some routes there is a price reduction if you travel after 09:30.
Note Canterbury has two stations, Canterbury West and Canterbury East. For a rail map including all stations in Kent click here. If you look at the map you can see the line from Chatham goes to Canterbury East, but you have to go from Canterbury West to Ashford
And as harleydonski says, it is just plain "Kent". It was in independent Kingdom in the Dark Ages, long before England existed, and it was demoted to a mere county.
I live in Kent and Chatham and Ashford are two places that would be BOTTOM of the places to stay in the county! Faversham is much nicer than Chatham and Sandwich nicer than Ashford or do a second night in Canterbury or go through Ashford station and on to Rye and stay there. No need to book. If you are travelling at the weekend, check that there are no engineering works (would mean added time and a bus replacement service).