Former Kingfisher Harvey Harry struck the only goal as Thatcham slipped to a 1-0 defeat in a game played at Burnham's 3G surface.
The winger cut in from the right and whipped a shot across goal into the far side of goal from the corner of the penalty area, giving Toby Fisher no chance.
The goal came on 42 minutes, just minutes after Thatcham had their best spell of the game. Mo Ceesay was put through on goal but rolled his shot agonisingly past the post, then saw his downward header from a corner held by the keeper.
Toby Fisher had earlier made a couple of routine saves as chances were few and far between.
In the second half opportunities were even rarer, though the heavy rain meant the game was played at pace on a zippy surface.
Jordan Alves tried his luck with a late free-kick but saw a deflection take the sting off the shot, resulting in a staightforward save, as Southall climbed to second in the table.
Team : Fisher, Gwavava, Daniel-Spray, Willmoth, Heholt, Blackwood, Tanner, Jones, Brown, Ceesay, Nyarko
Subs on : Alves, Bangura, Johnson. Unused : Hoath, Clark