Re: Thailand and Singapore
Can't help you for London to Thailand trip but from Thailand to Singapore try these airlines:
airasia.com
tigerairways.com
bangkokair.com
they have the best deals for whithin Thailand and the surrounding countries, thier websites are reliable, i have personal experiince with these airlines.
But, don't expect too good of a service, after all these are all budget airlines, selling tickets for a few tens of dollars, also the journey between Thailand and Singapore is very short, you'll just get into the plan, sit down, and then start getting ready to get off. :)