And the Internal Market Act has also been attacked as a power-grab, in limiting powers for the devolved capitals to determine standards over goods and services, in the shake-up following EU withdrawal.
The IfG said the replacement of structural funds created an opportunity to “put in place something that is more flexible and less bureaucratic than the EU system”.
But it added: “This should be done in a way that respects the devolution settlements and takes into account the devolved governments’ existing role in administering structural funds.
“Failure to do so risks further damaging trust between the UK and devolved governments at a time when inter-governmental relations are already strained.
“This could undermine the UK government’s key objective of binding the four nations of the UK closer together.”
The warning will fuel an existing row over the scale of funding, with the new scheme not to be launched until April 2020 – creating a one-year gap in spending.