Vernon Bogdanor, whose new book, Beyond Brexit: Towards A British Constitution, calls for a written constitution to respond to the pressures of leaving the EU, said reducing investment or changing the Barnett formula would produce “howls of rage”.

EU structural funds have been worth €900 million to Scotland since 2014, out of a UK total of €10.9 billion. A consultation on the UK government’s plans to replace EU investment funds is already more than three months late.

Government sources have said their intention is to replace a system where investment for deprived areas has been passed from Brussels to devolved administrations for allocation to one where local authorities and community groups apply directly to Whitehall departments, no matter where they are in the UK.

A demonstration against the poll tax which was introduced in Scotland in 1989

The plans have provoked anger in Edinburgh, and Scottish local authorities say UK ministers are “not playing by the rules”.

Meanwhile, the UK government has also been accused of undermining the Barnett formula by not announcing any windfall from new investment funds, including a Stronger Towns Fund aimed at economically depressed areas that voted for Brexit.

“In my view, the best thing is not to tamper with the Barnett Formula, since if you alter it, the beneficiaries won’t say thank you but the losers will howl with rage,” Bogdanor said.

“That happened with the Poll Tax… the losers howled with rage and brought down Margaret Thatcher. Best to let sleeping dogs lie.

“In any case, it’s very difficult to find an objective needs basis. How do you weigh the needs of a remote rural area of the Highlands against an inner city such as Liverpool? There’s no objective way of doing it.”

In his book, Bogdanor warns of the impact on the constitution from Brexit, with responsibilities that previously rested in Brussels but were administered at a devolved level now having to be shared across the UK to allow for a coherent trade policy.

“Brexit should be a constitutional moment for us, and we should begin with a charter on the powers and responsibilities of the devolved bodies, because we’ve done devolution in a very ad-hoc and unplanned way, sometimes in a state of panic,” he said.

“It’s not clear what powers in the economic and social field the government needs to hold and what they can let go to preserve an economic and social union.

“They’ve let go a lot to Scotland, and Scotland hasn’t used a lot of its powers but they keep wanting more. The SNP has sometimes used a supposed lack of powers as a grievance machine.”

Bogdanor added: “You can’t have four totally different systems of agricultural subsidies, particularly as agriculture is a basis of trade negotiations… if it had been known that we wouldn’t be in the EU then probably some agriculture powers would have been reserved.”

He said a proposal from the Welsh government for a “Council of the Isles”, where UK decisions on shared responsibilities would have to secure the support of at least one devolved administration, was “worth considering”.

But he dismissed calls for an English parliament or regional assemblies.

“The best practical way to achieve English devolution is by developing the Northern Powerhouse – combined local authorities with directly elected mayors,” he said.

Cuts to Scottish EU funding ‘risk Poll Tax rage’