Which might all be grist to the mill..in time, but IMO not now.
You do not have hard evidence to support your phone calls. My suggested draft focuses on irrefutable evidence, the vast majority of which has been generated by TfL.
I would not intend to expand on the draft unless something which is essential to the issue has been omitted. Frankly, if they can't see their error - in disregarding your reps, and let's be clear this is the issue - then IMO next step is their complaints procedure. IMO, they may not hide behind them having already followed prescribed procedure- which would otherwise deny you a second bite at the cherry- because the evidence shows they have not.
For the future, I am interested in your recollections regarding receipt of their correspondence, in particular a letter dated 12 July, carried by registered mail and being delivered on 19th. Unless there's something untoward at your end, this challenges any reliance upon the presumption of service at a time based upon the date of enclosed letters. But IMO this can be filed for later if required.