- A quick search on Trainline showed me that you can go from Paddington via Great Western Railways direct to Bristol Temple Meads Station in about 90 minutes
- You can go direct from LHR to Paddington via HEX, Lizzie, or Piccadilly line.
- To go to Kent from there, yes, you would return to Paddington, but that's easy since you just came!
- Then it looks like you can either take the underground to Victoria Station and Southeastern to Kent
- OR head to St. Pancras Intl from Paddington and take Southeastern to Kent. I have taken SE from St. Pancras and would probably do that. It's straightforward. They have an app, so you can buy direct.
Lots of people buy from Trainline but I only use it to scope schedules. I tend to use the train apps. Probably just preference.