http://www.tubeexits.co.uk/ seems to be an app which has this sort of information. The presentation of it and how good it is - I don't know. http://www.stationmasterapp.com/features.html does the same thing. I know for a fact Station Master was produced a while ago, not sure about Tube Exits, but The Telegraph ran an article about it in 2017, so probably then.
Hope this helps,
-Peter
I have two editions of that, one dated 2001 and the other, with "Completely Revised edition" on the cover, dated 2011. Both were priced at £1.95. One side shows inner London stations, the other outer London, with symbols and car numbers to show where the exits are. The earlier one may have had a connection with Stanfords, the map shop, as it includes a map and list of their shop locations. They seem to have been published by a company called Drumhouse Limited based in mid Wales, and are still shown as available from a company called mapsworldwide.com for 97p.There is (or was) also a diagram called "the way out map of the underground" (or similar). Can't vouch for its accuracy or usefulness as I never bought one.