Trains head to various stations in central London. Your ticket is usually issued to "London Terminals", which allows you to use any central London terminus (without specifying in advance).
The one complication is that if you want to use the faster trains (into St Pancras) you must have the "including HS1" endorsement on your ticket, which costs a bit more.
Where are you aiming for within London? There is no point paying the higher price for a HS1 service if your actual destination is at or near one of the other options (such as Victoria).
Canterbury West (CBW) and Canterbury East (CBE) are the two stations. CBW offers service to St Pancras (STP) and Charing Cross (CHX), while CBE offers service to London Victoria (VIC). Advance fares are as low as £10.10 for CBE to VIC and £12.50 for CBW to STP on the high-speed service.
Also to add, incase you have not yet happened across The Man in Seat 61 -- https://www.seat61.com/ -- you might find the website extremely useful. I do not know how much you intend to use trains to get around, but this is probably the single best website covering trains in the UK.