Yes it is part of a normal service. It used to run every week day at 09:22 from Charing Cross calling at Waterloo East, London Bridge, Orpington, Sevenoaks, Tonbridge, Ashford International and then all stations to Ramsgate via Canterbury West. I caught it one morning in 2018 on my way home from Stansted, having wanted to catch it for a long while although had never needed to travel back from London at that time of day before.
We flew through the fast lines at Paddock wood and Headcorn at such great speed that we arrived into Ashford early. I have no idea why they decided to run such a useful service at that inconvenient time.
In the next time table change it was cut back to Ashford only but the same calling pattern was kept. Until 2010 the original hourly fast services were non stop between Waterloo East and Tonbridge.
Unfortunately, there aren’t any other similar services which is a shame. The new franchise includes semi fasts, not quite the same as back in the day though. For now this is the only remaining Tonbridge - Ashford fast service.