If you live within half an hour's travel from King's Cross, eurostar does not take longer for door-to-door time. More pleasant and less weight restrictions too
Plane can do faster and cheaper door to door.
I admittedly am not optimizing for price--intra-Europe flights can be pretty inexpensive--but I'd much rather take the train than fly even if it costs a bit more and takes a bit longer.
I understand the feeling. I hate flying too, in particular cheap European airlines. Gotta admit that there is an inflection point though, maybe around a thousand kilometers, where trains are struggling to keep up.
I commuted monday-friday from London to Paris for a couple months, and if I were to fly I don't think I could take it.
The London-Lyon is disappointing. Better take a plane.
It depends on the speed of the service of course but, even with relatively high speed rail, a thousand kilometers is probably at the outside edge of where a train makes utilitarian sense.
However, my impression is that relatively few take it all the way from Boston to Washington DC. It's still about the same 1 hour flight that the shorter legs would be by air but now it's basically a full day of train travel. I've done it when I've just been happy to work on the train but it doesn't really make a lot of sense most of the time.
Even with a train service like the Shinkansen, getting from Tokyo to, say, Hiroshima is over a 5 hour train ride for a distance of a bit under 1,000 km.
I like taking trains in Europe and Japan but there's an upper distance limit for when they make utilitarian sense. (For London to Brussels or Paris though, it's hard to imagine why I'd want to fly even if it were a little cheaper.)