Rather oddly the Southeastern Twitter feed on the BBC website at
https://www.bbc.co.uk/news/topics/cywd23g0gyvt/southeastern indicates that a limited High Speed service was able to operate from about 16.30, albeit with a queueing system in operation at St Pancras, but both Real Time Trains and Open Train Times appear to show that all Southeastern High Speed trains were cancelled for the rest of the day.
Real Time Trains only lets you look up the departures from a station for the last 7 days, but you can look up a train longer ago by clicking on that train from any day in the last 7 days and then manually changing the date to the one you want in the web browser once you've got the timings for that train on your screen. For example, the timings for the 16.25 St Pancras-Faversham for today are at
http://www.realtimetrains.co.uk/train/W00187/2019/01/23/advanced, and you can get the timings for that train for 15th January by simply changing the date:
http://www.realtimetrains.co.uk/train/W00187/2019/01/15/advanced
It also seems odd that Eurostar trains were still able to run, albeit with delays of up to 90 minutes, even though AFAIK they share the same tracks as Southeastern High Speed for most of the route.
