This was tried out a few years ago, but was cut back because nobody used it: https://stratfordobserver.co.uk/news/town-needs-direct-rail-link-to-london-says-culture-bosses/

To be fair, the area is already quite well served. I can't really see this being viable, but am willing to be proven wrong.

Services are being increased; it'll be interesting how it all works out: http://www.stratford-herald.com/95688-number-stratford-london-trains-will-double.html

A Stratford to London service is being reintroduced - to fit round performances at the RSC, naturally: https://www.bbc.co.uk/news/articles/c0qvg4z872do

I give it 12 months.