I think they do somewhere on the DLR (Canary Wharf?) but at Guildford they don't, always use platform six, away from the third rail, in my experience. Somewhat frustrating when trains are replatformed from 8 to six, when they actually stop at the opposite platform seven.
I notice some stations have single line track that serves platforms on both sides, Norwood Junction is one.
Do any trains get listed as stopping at both platforms with the doors on both sides opening?
The south facing bay at Carlisle used to see one train that opens doors on both sides, but not at the same time. It arrives as 2x153, the doors open on the side not normally used to allow passengers to alight. The set is then split and on the outer set the doors opened on the normal side for the return service down the coast.
It's done deliberately to stop people boarding the unit that's being taken out of service.
I'm not sure if they still do this (M-Th). the reason was that the 153 was used to strengthen the 158 on the first S&C the following morning. Since the introduction of the loco hauleds this might be a thing of the past.
There are two such platforms on the Cumbrian coast: Ulverston and Sellafield.
I am not sure about Ulverston
Also Ascot P2 shares a face with P1, not sure if that gets used on race days at all.
Platform 5 at Derby (the bay) is an example of where the side the doors open has changed in the last few years for safety reasons - so the recently and expensively rebuilt canopy on the platform is now on the wrong side to where you actually board
As far as I'm aware whilst there's examples on London Underground (eg Stratford Platform 3/3A) and DLR (Canary Wharf, all three tracks) there's nowhere on the National Rail network that the doors open both sides on a train in service- despite quite a lot of examples where they could.
Derby platform 5 is particularly unusual as XC services open their doors on the platform 4 side and EMT on the platform 6 side.