My wife and I are US citizens. My wife has been accepted to study abroad as an undergraduate for 1 school year (September'16 - May'17) in London, UK under PBS Tier 4 Student Visa. I intend to travel there with her. I will be her primary means of financial support while there. I'm a software engineer, so my work will be done entirely remotely online for a US based company involving only US bank accounts (I mentioned this since this link suggests that these are the main concerns with remote "work" in the UK.) Also as I understand it, I can apply as a dependant to travel to the UK with her.
My question is this: will I be allowed to work remotely for a US company receiving payment to a US only bank account while living in the UK as a dependant of a US exchange student? If not, then under what visa/immigration-policy would this be doable?