I hope I'm not too late on this post!
Awesome project! I think feasable, but you'll need to either be super flexible timewise or get a bit of planning ahead of leaving. The problems are the visa for China, and possibly Vietnam if you wish to see it. The Lao and Cambodian visas you can buy at the border, with cash and photos, but not the other two. So either you waste time in the embassies in Thailand then await those visas, or you get them prior to leaving UK, which is what I'd recommend. You can in this way concentrate on having fun
I would recommend to avoid doing a lot of in and out of countries, because this would bring attention to yourself at borders. SEA and East Asia are areas of the world where a lot of traffic of a sorts is occuring. Don't think you want to experience an officer's curiosity...
Is your budget amount in Euros, dollars or pounds ? Even being in dollars, you still have enough : 4k = $50 a day. You can live for as low as $15-$25 in most SEA cities, and that includes meals-lodging-inner transport. International transport is a bit higher.
As for time frame, 3 months is fine but of course, if you could stay longer that'd be even better. Asia's life flows at a slow pace and that gets to you early in your stay. Plus transport in Asia is a painful uneffective neccessity that will slow your plans down anyways. Plus there is so much to see and do ! Plus China is so big. The very least number of weeks to visit a country there would be 2 weeks. For example, I did 2 weeks in southern Laos; 3 in the northern half of Vietnam and that was too quick ! I would have needed to double the time, in order to see the whole country.
Lastly, is it even possible to just get a 1 way plane to SE Asia and tell them that we are going home by any means possible bar another flight? and promise them not to outstay our welcome?
I can't answer this. I know you are required to have a proof you will exit the country, but I'm not sure they do in fact ask for it at the border. Having been to China either, but I'd think they are quite stuck on procedures...