On an Any Permitted ticket, you can go via London provided that you get
to Reading via Staines (e.g. Gatwick to London Bridge, W&C line,
Waterloo to Reading).

I'm sure a Not London ticket would also let you go Gatwick, Clapham
Junction (change), Reading (via Staines). But if it's an Any Permitted
ticket, I'm confident there's nothing stopping you going via
Paddington...