Wallwork quit the World Class Performance Programme, complaining she had no say in her own career path. She is the second top player to leave after Imogen Bankier, who now competes in Scotland.
In a strongly-worded open letter posted online, Wallwork said: "I feel I have no voice or direction in the way my career is going and find myself in an impossible situation other than to remove myself from the World Class Performance Programme."
Wallwork said that her concerns had fallen on deaf ears, adding: "'Continue with the programme given to you or submit your resignation' was an ultimatum recently given to me.
"I feel this indicates insecure, untrusting and incapable leadership and I am not prepared to be dictated to and therefore feel I am unable to continue with a programme in which I have no confidence."
Badminton England responded on Monday night, saying: "Jenny’s decision has taken us by surprise and we are disappointed with the manner in which she has chosen to communicate it.
"We had discussed Jenny’s programme and how it should look in considerable depth with her in the last couple of months and thought we were moving forward positively.
"Indeed, we felt we had received strong signals to this end.
"All players have a voice and are listened to as decisions are made concerning their individual programmes.
"However, devising the GB programme is a huge and complex undertaking, encompassing many players, and we are dependent on everybody working together to achieve our goals."
Wallwork and Nathan Robertson narrowly missed out on a place in Britain's Olympic doubles team, losing in qualifying to Bankier and Chris Adcock.
She has not yet stated whether she will attempt to continue her career independently of Badminton England.