Peter,
Svetlana is mostly right. The very cheap beach bungalows that we all envision; basic bungalow, right on a beautiful white sand beach, clear water lapping at the sand, are getting difficult to find, but not impossible. I would get myself to Krabi town and go into the many travel shops and tell them what you are looking for. They will have photos and descriptions of dozens of islands and beaches that are just what you are looking for. Most are just too small to have a website and advertise. But, you can see what is out there by doing a search; type in 'koh jum thailand', 'koh lanta', 'koh dok mai',
'andaman sea'. There are photos of Joy Bungalows and Woodland Resort on Koh Jum that look like what you are describing.
Another option is to visit the small beaches north of Nha Trang, VN. Dai Lanh Beach, 83km north of N.T. has bungalows on the beach for under $5/nite. Jungle Beach is 60km north of N.T. $10/nite. Paradise Resort is on Doc Let Beach, 30kn north of N.T. 3 bungalows are right on the beach, $12/nite includes 3 meals/day.
Hope this gets you pointed in the right direction.