I'm sorry, that sounds really uncomfortable.
Maybe it is peculiar to the Piccadilly line? I am on the Victoria line and always get offered a seat.
If it is really crowded though, people sitting can't always see who is standing in the doors - what bugs me now about the tube is that no one moves down, so the entryways are always heaving but along the aisle it is often empty.
Also, if you can position yourself to get on at either end of the tube, you are more likely to be seen/find a seat as these carriages are less crowded.
There has also been a real increase in people going from carriage to carriage asking for money (on the Vic line at least) and as a result, sitting passengers do seem to keep their heads down to avoid eye contact.
Also, now you can get wifi* on more trains, most everyone is nose down in their phone, so yeah, speak up!
(A long-winded answer to a problem you shouldn't be having though!)
*edit to add - I mean mobile service