In message , Jack Taylor
writes
Crossing platforms *shouldn't* be too much of a problem. The Southern
service from Gatwick (www.southernrailway.com) will normally arrive at
platform 12, whilst the South West Trains stopping services to
Walton-on-Thames (www.swtrains.co.uk) usually leave from platform 11, which
is the other face of the same platform.

If that is the case, then the OP is extremely fortunate. To cross from
one island platform to another at Clapham Junction with heavy bags is
*extremely* tedious and involves *lots* of stairs.

Incidentally, I did this change a few months ago, from a "Connex-ish[1]"
train from Gatwick to one on the Esher/Walton/Weybridge line and it
*did* involve changing islands. Was I unlucky?

[1] It really do lose track of what these TOCs call themselves this
week.
--
Roland Perry