If you will be travelling around Asia for 3 months will it be more economical to buy a multi-ticket in advance in the UK or to book the flights in Asia as needed?

It definetly won't be cheaper to book tix while in Asia. Some of the domestic only carriers are best to buy when "in country" but any major flights won't be any cheaper. My girlfriend and I did a tour last year. Cathay pacific has a stellar package called the all Asia pass. Basically it's all the destinations in Asia you care to book for up to 30 days. We paid 1700$ last year. The only drawback is you have to have all your flights booked before you go, and you can't change anything.