The letter said the UK government's Pride of Place town centre improvement programme had caused "considerable unhappiness" amongst Welsh Labour Members of the Senedd (MSs).
It said it was a "UK government programme operating in a wholly devolved area that is being designed and delivered from Whitehall".
The letter criticised the use of the Boris Johnson-era UK Internal Market Act to "impose" the new programme.
The law was controversial in part because of the powers it gave the UK government to spend money in areas that are otherwise controlled by the Welsh government.
Ministers in the Welsh government attempted to have the law overturned in the courts, the letter said, because "the Internal Market Act represented an unwarranted attack on devolution".
"For our own government to then come in and use the very same powers to act in devolved areas is at best deeply insensitive, at worst a constitutional outrage," it said.
"If this was being done by a Tory government we would be calling for a judicial review. This must never happen again".
"Wales needs and deserves to be treated as an equal part of the UK and the UK government has a responsibility to act to deliver this equality."