The plans are opposed by the District Councils’ Network, an umbrella group for such councils, which says there is “little evidence” from past reorganisations that taxpayers’ money will be saved.
Hannah Dalton, vice-chair of the network, said the “creation of mega councils” could prove “the opposite of devolution”.
She also warned the reorganisation could spark a “period of turmoil which will prevent councils from focusing on the local services that drive new homes, jobs and reduce pressure on the NHS”.
The Conservatives said Rayner’s announcement was part of a plan to “strip councils of their powers” and to impose reorganisation from Westminster “without local consent”.
However, the proposals have been welcomed by the County Councils Network, which says its members “now recognise the need to embrace the benefits” of devolution in the face of “significant financial challenges”.
Cllr Louise Gittins, chair of the Local Government Association, said “genuine devolution of powers and resources can play a huge role in promoting inclusive economic growth, creating jobs, and improving public services”.
She said her members were “open to change” but “remain clear that local government reorganisation should be a matter for councils and local areas to decide”.
Since returning to office in July, Labour has announced four devolution deals: Greater Lincolnshire, Hull and East Yorkshire, Devon and Torbay, and Lancashire.