Hours after Theresa May insisted at prime minister’s questions that Surrey had enjoyed no preferential treatment, one of the released letters and emails showed the chancellor had spoken to the communities secretary, Sajid Javid, on the council’s behalf.

Hammond, who represents the Surrey constituency of Runnymede and Weybridge, wrote to the council’s deputy leader, Peter Martin, in September to sympathise about funding difficulties, saying he would “take this up with Sajid Javid”.

The correspondence shows that another Surrey MP, Jonathan Lord, wrote to the council in November saying he had discussed the issue with Javid and “he’s doing something for us”.

In an email to the council’s leader David Hodge and fellow Surrey Tory MPs in January, Lord suggested Javid might have “£40m hidden under the departmental sofa” for the council, and suggested other councils’ budgets could be trimmed to help.

The correspondence, released following a freedom of information request from the BBC, follows a long and public standoff between by the Conservative-run council and Javid’s department over what Hodge said was a funding gap to pay for social care.

Hodge promised to hold a referendum of Surrey residents on imposing a 15% rise in council tax to make up the shortfall. However, last month this was called off at the last moment.

Leaked text messages passed to Labour last month prompted Jeremy Corbyn to accuse May at prime minister’s questions of buying off Surrey with a special deal, something she denied.

Following the release of a recording in which Hodge told fellow Surrey Conservatives about a “gentleman’s agreement” with ministers, Corbyn reiterated the accusation at PMQs on Wednesday. May again denied Surrey had received special treatment.

The new documents show a concerted lobbying effort by Surrey MPs, among them Hammond. Other Surrey MPs to lobby for the council included Chris Grayling, the transport secretary, Michael Gove, Crispin Blunt and Dominic Raab, the correspondence showed.

It also highlights the extent of anger felt by Hodge over the funding issue. In one letter, he accuses Javid of “some seriously muddled thinking”, and warns of the political consequences if an agreement is not reached. “We will see the largest Conservative group in the country pitted against a Conservative government, and we will be blunt about where we think the blame lies,” he warned.

Writing to Hodge, Hammond had said: “I recognise the challenges you are facing in Surrey, and the apparently harsh treatment that the funding formula delivers, and I will take this up with Sajid Javid.”

An email from Lord in November suggested Javid and Hammond were seeking to help the council. “I have spoken to Sajid J, and he says he’s doing something for us,” Lord wrote. “Won’t be drawn on exactly what. Says that Philip H is being supportive and will be signing off on things for us.”

But a subsequent email from Lord in January said he was “extremely unimpressed” Javid had not “come up with the goods”.

He wrote: “If Saj was imprudent enough to not have £40m hidden under the departmental sofa just for this sort of emergency/problem/‘outlier’ emerging from his department’s draft settlement, then I assume, if he is a man of his word, that he must have done his best to put a strong case to the Trreasury

“If all his local government settlement money is really allocated, if the Treasury is refusing to help out, and if he can’t find a pot of money for the ‘missing’ learning disability grants, then Saj still has the option of adjusting all the other council settlements down very slightly in order to accommodate the £31m needed for Surrey – and I think he should be encouraged to do this.”

The shadow communities secretary, Teresa Pearce, said May should “come clean” over the deal. “Despite Theresa May’s claims to the contrary, this is more evidence of the Tories’ secret deal with the leadership of Surrey county council,” she said.

“We need full disclosure of the terms of the deal and reassurance that all councils will be treated the same way, not just the lucky few the Tories favour.”

However, a government spokesman said the discussions were nothing exceptional.

“As we have repeatedly made clear, there was no special deal for Surrey county council and they will not receive any extra funding that would not otherwise be provided or offered to other councils. To imply the opposite is simply untrue,” he said.

Javid’s department discussed funding settlements “with councils across the country, of all types and all political parties”, he added. “This happens every year, involves councils making representations to the government, and has always been the process.”