Your first stop is The Man in Seat 61, a site dedicated to train travel around the world and getting there from England by train in particular. The focus is on train travel but overland alternatives (buses, boats, etc.) are mentioned when trains don't cut it. So read London to Thailand overland.
Starting from Thailand, crossing Myanmar is pretty much impossible. So you need to cross into Laos or Cambodia, then Vietnam, then China (you can cross Laos directly into China, but it makes for a complex trip). According to Seat61, either option lets you travel from Bangkok to Hanoi in two days, with a 3-day trip through Cambodia being a more comfortable option. Seat61 has a map of trains and connecting buses in the region.
From Hanoi, it's all plain sailing, or rather plain train riding, through eastern China, then on the Trans-Siberian to Moscow and from there wherever you want to go to in Europe. Again Seat 61 has the details; there are daily connections between Hanoi and Beijing, with a twice-weekly direct train taking two days. The Trans-Siberian travels the 9000km from Beijing to Moscow in 6 days.
Alternatives for this part of the journey are scarce. While not as impossible as Myanmar, western China (Tibet and Xinjiang) is restricted to most travelers. You may or may not be able to cross Xinjiang and into Central Asia, then proceed west either through Russia or through Iran into Turkey. This depends on your nationality, your taste for adventure and how much time you have. You may follow one of the many Silk Road itineraries, if the journey is that much more important than the destination.