George Osborne’s “northern powerhouse” plan to rebalance the UK economy away from London and to the north of England has been dismissed as “smoke and mirrors”.

A new report by the Liberal Democrats argues that without real investment, the northern powerhouse is just a buzzword that is stronger on rhetoric than substance.

Osborne coined the term in 2014, when the Conservatives were still in coalition with the Lib Dems, who are long-term proponents of devolution. The party now argues the project is just “a smokescreen to hide cuts that have been implemented across communities and local government”.

As part of the northern powerhouse agenda, the government has so far agreed devolution deals worth £30m a year for 30 years with combined authorities in Greater Manchester, the Liverpool region, the Sheffield region and the north-east. Another, worth £15m a year for 30 years, has been agreed with Tees valley, and the West Midlands has negotiated a deal worth £36.5m a year.

But the report, entitled The Northern Powerhouse: Smoke & Mirrors?, argues that the additional funding doesn’t compensate for cuts made to council budgets. From 2010-11 to 2015-16 there was a 40% estimated real-terms reduction in central government funding to the relevant local authorities, the authors claim.

“There is very little revenue funding associated with the devolution deal projects. The vast majority of income relates to capital income over the next 30 years – much of which the local authorities would have received in one form or another anyway. This is more than offset by cuts to the budgets of first tier and joint authorities within the city regions,” the authors argue.

The report also criticises Osborne for forcing elected mayors on local authorities as a condition of devolution. John Pugh, MP for Southport, said: “These are unwanted elected mayors, adding a further level of power that central government can dictate to. They are inherently undemocratic, forced in place against the will of referendums, or, as in the case of Merseyside, without any referendum, taking even more power away from the citizens of the region.” The mayors will be elected next May.

Nick Clegg, MP for Sheffield Hallam, was deeply involved in the northern powerhouse plan when he was deputy prime minister. But he is now critical of the transport investment announced, particularly Osborne’s commitment to building a fast line between Manchester and Leeds, known as HS3. “The northern powerhouse is failing to live up to the dream that we envisioned in the coalition. Instead, it is being used as an excuse to put in place piecemeal devolution and changes but with the rhetoric of great change. The recent announcement to ‘green light’ HS3 proves this. The link from Manchester to Leeds is ignoring areas like Liverpool and Sheffield, who are being left off the transport grid,” said Clegg.

James Wharton, Conservative MP for Stockton South and the minister for the northern powerhouse, said: “It is a shame that this highly political report peddles such negative and misleading lines rather than engaging with and supporting a project that is in the interests of everyone who loves and works in the north of England. They ignore the transformational rail investment already announced, the investment funds agreed and the devolution deals which will bring millions in investment and real control to areas outside the capital. It is no wonder so few people in the north vote Lib Dem any more.”

He insisted the northern powerhouse would not disappear if Osborne is replaced as chancellor. “It’s too established now,” he said.