Unfortunately for Thomson, here on the DIS, you are in a community with collectively a lot more knowledge of the Disney empire, than themselves
I should get back in touch with Thomson ASAP
Ask to speak to a Manager and request their contact details (Name, location, department etc)
Advise them that THEY should contact Disney on your behalf, since your contract is with TUI
Mention also that you have been in contact with lots of people who have already used the new Disney booking system with success and assure them that MDE is definitely operational for U.K.
(I have just finished booking 18 ADR's for August, some for 13 persons, using MDE, with no problem)
Request a formal response within a reasonable time (say 24 hours)
If they still cannot sort it, advise them that you will move it up the ladder on their behalf, to the MD of TUI in an effort to highlight the unacceptable customer service and possibly to pursue compensation.
Managing Director of Thomson Holidays is David Burling
david.burling@thomson.co.uk