ska invita
back on the other side
not sure about train times but on the south bank Sheerness/Minster (essentially two ends of the same beach) is geographically closer, and quicker in a car - the far end of Minster is the nicest bit of the stretchIf a "proper" beach means one where you'd actually want to hang out and where you might want to go into the water, and if "closest" is measured by "quickest time to get there on public transport from south London" then investigations carried out be me in the past have determined Whitstable as the one on the south side and Chalkwell (Southend-on-sea) on the north side.
North coast Chalkwell looks like a big proper beach, though on the map there is a little thing called Thorney Bay Beach on Canvey that does look proper and accessible (as opposed to something like Egypt Bay Beach on the south, which is inaccessible) and is closer
Sheerness does have a station, but I cant see one near Thorney