Leaving a car on-street even if in a marked bay which permits your car to park there, then leaving it for weeks on end is just asking for big trouble in London, because bay suspensions are frequent. Frankly, TfL should NOT have moved you car to a Tower Hamlets permit-only bay; they should have towed the car to their pound. This means you would now have a single PCN, a tow charge, and 20-odd days of storage at £55 a day, so still a large sum.
Your statutory grounds against the TH PCNs, ssuming they were served under the Traffic Management Act 2004 is found in Regulation 5(4)(c) in the The Civil Enforcement of Road Traffic Contraventions (Representations and Appeals) (England) Regulations 2022
"(c)at the time that the alleged contravention occurred, the vehicle in question was in the control of a person who did not have the consent of the owner;"
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TfL, for reasons known only to themselves, moved your car into a council bay, whereas they should have towed the car to the pound. The TfL PCNs will be far more difficult to refute in my opinion.