Mr Corbyn has written to Sir Mark Sedwill warning it would be an “anti-democratic abuse of power” if the Prime Minister was to deny voters a choice on Britain’s EU future in an election campaign.
The move comes amid reports Mr Johnson could seek to hang on long enough to ensure Britain is out of the EU before going to the polls if he is defeated in a vote of confidence when MPs return in September.
As it stands – under the latest extension to the Article 50 withdrawal process by the EU – Britain is due to leave on October 31.
But with a wafer-thin Commons majority of just one, Mr Johnson is vulnerable to defeat if, as expected, Labour table a no-confidence motion early next month.
If that happened, under the Fixed Term Parliaments Act, he would have 14 days to win another vote of confidence or, if no other government could be formed, face a general election.
His top adviser Dominic Cummings is said to have argued that would still allow him to set an election date after October 31, by which time the UK would be out of the EU with nothing a new government could do to stop it.
In his letter to Sir Mark, Mr Corbyn said such a course of action would be “unprecedented” and “unconstitutional”.
He said the Cabinet Office’s election “purdah” rules make it clear that policy decisions on which a new government “might be expected to want to take a different view” should be postponed until after polling day.
He asked Sir Mark to confirm that if the UK is due to leave the EU without a deal while an election is under way, the Government should seek another time-limited extension to Article 50 to allow the voters to decide.
“Forcing through no-deal against a decision of Parliament, and denying the choice to the voters in a general election already under way, would be an unprecedented, unconstitutional and anti-democratic abuse of power by a Prime Minister elected not by the public but by a small number of unrepresentative Conservative Party members,” he wrote.
“A Labour government will never support a no-deal exit, so would of course ‘want the opportunity to take a different view’.”
Labour's shadow transport secretary Andy McDonald echoed comments from his boss, telling ITV News "it would be totally and utterly unconstitutional - it'd be an unprecedented move and entirely undemocratic for one government to bind another once a general election is called".
Mr McDonald added: "That's why Jeremy Corbyn's written to Mark Sedwill - the head of the civil service to say this is totally wrong and he's the custodian of the rules, and asking him to intervene to make sure that doesn't happen."
But Brexiteers argue Parliament has already voted to leave the EU, voting to trigger the Article 50 process and passing legislation setting Britain’s withdrawal date for October 31.
Officials said that Sir Mark would be replying to Mr Corbyn, but senior Tories dismissed the Labour leader’s letter as a “political stunt”.
A senior Conservative source said: “Jeremy Corbyn will do anything to get his hand on the keys to number 10. No amount of letter-writing political stunts will change the fact that politicians don’t get to choose which public votes they respect.”
On the possibility of forming a coalition government in the event of a no-confidence vote, Mr McDonald said: "We'll put a plan together and it's up to them (SNP and LibDems) whether they want to support us."