Mounting pressure on town halls to gear up for Brexit is because the government is failing to deal with its burden, the leader of Greenwich Council has said.

Local government secretary James Brokenshire said last week that councils in England will receive £56.5m to help them deal with the EU split.

Every council will receive a share of the pot, but more cash will be given to authorities facing the impact from local ports.

Greenwich Council’s leader said the authority’s £210k handout will not be enough to deal with the problems.

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“It very much feels like the burden to resolve the pressures of Brexit has been passed to local councils because the government has so abjectly failed to do it,” Cllr Danny Thorpe said.

“Whilst we are doing our best to prepare, clearly we face enormous risks and challenges moving into a very uncertain period.

“We’ve got a team ready and last night we had a presentation from each department looking at things like school dinners, where supplies come from, petrol and fuel – because the police would come to us if they don’t have enough. We’d use Birchmere as a depot.

“There are issues about adult social care and the drugs people would need. There’s no way it would be enough, we don’t know what would happen.

“With City Airport across the water that would be a border, that would inevitably have some implications. On all the modelling that we’ve seen so far – if the boats were to be stopped, forget the airport, the A2 would back up quickly.”

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Council leaders have been sent a Brexit checklist, calling for impact assessments to be carried out on vital local services such as social care.

The checklist reads: “Members will want to be assured that the council has undertaken an assessment to consider the potential impact on your regulatory services, including putting contingency plans in place to respond to increased demand.

“Members will want assurances that their council and any strategic delivery partners that they have impact assessed their supply chain and that appropriate mitigation plans are in place in order to assure the council of their preparedness for any identified risk to the delivery of statutory services.”

In a written statement to Parliament, Mr Brokenshire, who is also the MP for neighbouring Old Bexley and Sidcup, said: “Local government will play a critical role in making a success of Brexit at the local level.

“My department is committed to ensuring councils have the support and the funding they need to prepare for an orderly exit from the EU and do appropriate contingency planning.”