With respect - I think the BMA know an awful lot more about trust between patients and medical professionals than either you or I. And trust between a medical professional and a patient is something that rests at the level of an individual - so the notion that a different patient has trust is irrelevant when considering trust in the context of the patient sitting in front of you as a medical professional.
The BMA may think they know something but I think it should be up to the public to decide about charging fees, not the BMA. The BMA are not usually facing the problems ordinary members of the public face - most of their members probably opt for private healthcare.
My view is that necessity means people have limited choices even if fees are charged for treatment or a penalty imposed for missing appointments - if you want your illness or problem to be assessed and treated by someone qualified and trained in medicine you have to see a medical professional regardless of whether you feel you trust them or not because you have paid something towards treatment. Hopefully self-preservation will kick in for the ill person and they will go to a doctor (plenty to choose from) even if they have to pay, and ignore any feelings of distrust caused by payment of fees. If they don't want to go to the doctor due to distrusting all doctors they have to pay for, not much anyone can do about that.
Whether you trust them or not based on having to pay a fee doesn't alter the fact that seeing them is your only option if you want to be treated by a qualified professional. At least that's been my experience with private healthcare - you get the diagnosis and treatment options and then decide if you want to go ahead. Same with NHS - you can't trust the doctor to get it right in the NHS as medical treatment is often figured out by a process of elimination of possible conditions through tests and guesswork and somtimes you are unlucky and your doctor has not had the particular experience or has not read a particular article or can't recall it if they have read it in order to diagnose correctly. Sometimes you are unlucky and the test comes back with a false negative. I have experienced misdiagnosis from the NHS.
Luckily my mum is a doctor (retired) and therefore either she has recalled some obscure article she may have read or she has chatted with colleagues and relatives who are still doctors and between them someone has recalled something to figure out the reason for certain symptoms for people in our extended family, whereas the official NHS doctor or the private doctor being consulted by the patient has not figured it out yet. Whether fees are being paid towards medical treatment has been irrelevant in this process, other than you get quicker access and treatment if you pay - either via insurance or personally.