"Now that we know the UK will be leaving the EU we will be taking urgent steps to ensure that the UK Government protects Cornwall's position in any negotiations," council leader John Pollard was quoted as saying on Cornwall's official governmental website.
"We will be insisting that Cornwall receives investment equal to that provided by the EU programme," which has averaged £60 million ($113 million) per year over the past decade, Pollard said.
Cornwall can hardly afford to go without the annual EU transfers or equivalent compensations by the British Government: The county with more than 500,000 inhabitants is considered one of Britain's poorest regions, and experts say further funding cuts could be catastrophic.
In a 2014 study by research community Civitas found that impoverished counties such as Cornwall would have most to lose from Brexit. The EU particularly supports poorer regions and member states with its subsidies - which is why the poorest in Britain may feel the lack of money being transferred from Brussels most.
"Cornwall is a major beneficiary of EU spending so if Britain were to leave then the Treasury would have to take great care in ensuring its local economy was not crippled as a result," Jonathan Lindsell, one of the study's authors, explained in an interview with the Western Morning News after the study was published in 2014.
But such warnings did not deter Cornwall residents from voting for Brexit.
Leave campaigners had previously reassured the county that it would not lose any subsidies if it left the EU. However, Cornwall officials are now worried that such reassurances might have been little more than ill-thought-out promises.
"Prior to the referendum we were reassured by the Leave campaign that a decision to leave the EU would not affect the EU funding which has already been allocated to Cornwall," the council wrote in a statement on Saturday. "We are seeking urgent confirmation from Ministers that this is the case."
Cornwall officials' fears are not unjustified: Only hours after helping to convince the British to vote for Brexit, the leader of the UK Independence Party, Nigel Farage, appeared to show uncertainty whether all promises would be kept.
Some Brexit supporters had previously told voters that the US$470 million the British allegedly transfers to the EU each week would be allocated to the national healthcare system in case of a Brexit.
Besides immigration, the desolate state of Britain's healthcare system (NHS) significantly contributed to anti-EU anger, as Eurosceptics blamed the European Union for costing the country too much and wasting resources that could be spent domestically.
But at the weekend, Farage suddenly said it was a "mistake" to have promised allocating US$470 million to the NHS and distanced himself from that campaign slogan, saying he had never agreed to it.