Another option would be to commute from London Waterloo, which is a direct train, but it is a slow line.
I believe the train from Waterloo also stops in Clapham Junction, and Richmond. If deciding that paying the premium to live in/commute around London is worth it, I'd suggest checking out Richmond. I personally wouldn't describe it as "trendy", as that's more of an East London vibe.
But Richmond has a very nice feel to it, sort of village-y with nice parks/green spaces, access to the river, a variety of restaurants and highstreet shops, with access to trains, london overground, district line. It will be relatively expensive compared to some of the places mentioned already (Reading, Ascot)-- I think last time I viewed a 1 bed flat in that area it was hovering around the £1000/month price point. But it is a lovely bit of London if that's what you're looking for.
Would make the commute longer than your suggested 35-40 minutes, as the train journey alone would be 45 minutes.
One thing I'm becoming more and more aware of is that a "standard" London commute is about an hour. It's also definitely worth investigating what other options you would have in terms of public transport to/from Bracknell if you will be using public transport, as sometimes it's useful to have more than one way to get from A to B at the end of the day.
