The service exists but has been cut substantially - it's now an irregular timetable at something less than one an hour. But it still involves the M25, and that is the problem.

Stick with rail all the way, possibly taxi from Euston to Paddington if you prefer, though it is unlikely to save you time over the "shallow" Tube. You don't want to mess with the motorway traffic around London in the morning peak. There is just too much of a risk of problems.

OTOH, if your journey is on a Saturday or a Sunday, I'd go with coach - it doesn't get busy until a bit later in my experience.

Neil