The letter from shadow paymaster general John Glen asks whether the PM or his chief of staff, the former civil servant Sue Gray, had requested the pass for Lord Alli.
He has also asked for details on whether any other donors have received security passes for Number 10 and if other temporary passes have been issued.
“A Downing Street pass should be a privilege reserved for those that require access for work, including civil servants and special advisers, not those requiring occasional access,” he wrote in his letter.
“It is therefore deeply concerning that a pass was granted to a Labour donor providing unfettered access to the heart of government after significant cash and non-cash donations were made to the Labour Party.”
Mr Glen previously said it was “disappointing” to see Labour “only attempting to act on their culture of cronyism after feeling the pressure in the media”.
A No 10 source has confirmed Lord Alli held the pass when he attended a post-election reception in the Downing Street garden, but wouldn’t say why he was given the pass or why it was then given up.
Lord Alli has donated more than £500,000 to Labour over the past 20 years and was the party’s chief fundraiser for the general election.
The TV executive was appointed to the House of Lords by Tony Blair in 1998 and has recently led fundraising for the Labour Party, as well as donating to individuals including Prime Minister Sir Keir Starmer.
It comes after Chancellor Rachel Reeves was challenged over Labour donor Ian Corfield’s appointment to a civil service position in the Treasury.
Mr Corfield – who has previously donated £20,000 to Labour MPs, including £5,000 to Ms Reeves last year – was given a temporary job focused on organising an international investment summit taking place in October.
Labour had defended the appointment as “perfectly appropriate” but it is understood Mr Corfield has now moved to an unpaid advisory role.
Shadow Treasury minister Laura Trott previously called the appointment a “clear conflict” and urged the prime minister’s independent ethics adviser to investigate.
Civil service sources told the “hundreds” of officials are appointed through the post-election “exceptions” process – where time-limited jobs can be filled outside of usual recruitment processes.
They also said Mr Corfield’s appointment was signed off by the independent Civil Service Commission.
News has asked the government to comment on Mr Corfield’s contract status.