Whilst removing the rust from the central crossmember, I realised that the supports were acting as mud traps. After poking around with a bit of wire to get all the dried mud, grass seeds and rust flakes out of the tiny drain hole at the bottom, I finally decided that it would not make much structural difference if I removed the lower part of the bracing.
One has to be careful not to remove too much of the metal, but with the careful use of an angle grinder, at least now the inside of the chassis rail can get a decent coat of paint where there was previously just a layer of rust! Also there is now less likelihood of mud being trapped in this area. The thing is, even if you don't do any off-roading, it's not a good idea to have recesses which trap dirt, especially in a steel chassis. The mud or dirt attracts water, and water + steel = rust. In the UK in the winter, the roads are gritted with salt, and this causes steel to rust even more quickly.
Another couple of areas which can act as mud and rust traps are on top of the chassis at the rear: the "arms" on either side of the crossmember just in front of the petrol tank.
I decided to cover these recesses with some scrap steel plates. Before welding the area closed, I drilled a 6mm hole into the chassis top rail to allow any welding gases to escape.