Dominic Cummings revealed on Friday in a blog post, that he told Johnson he deemed his plans for donors to pay for his renovations, were "unethical, foolish, possibly illegal".
Labour's shadow home office minister Jess Phillips described the Mr Johnson and Mr Cummings row as "scrapping between two very powerful men who seem more interested in who's lying about what and who's leaking what than the substantive of the issue".
"You've got the former most senior adviser to the prime minister saying he's fallen well below the standards of integrity that are needed for the office of the prime minister".
© 2021 Getty Images LONDON, ENGLAND - APRIL 21: UK Prime Minister Boris Johnson leaves 10 Downing Street to attend the weekly Prime Ministers Questions in Parliament on April 21, 2021 in London, England.
The Labour Party called for a full investigation into the matter.
"Whether I back Dominic Cummings's view or Boris Johnson's view, what we need is a proper independent inquiry where it isn't about two boys fighting, it's about taxpayers in our country". No 10 says the cost was met by Boris Johnson.
Cummings said he was not responsible for leaks over the cost of the refurbishment and over Johnson's private communications over the sourcing of COVID-19 ventilators.
Mr Johnson lives in the flat above 11 Downing Street with Ms Symonds - a move echoing a number of his predecessors as it is bigger than the accommodation above No 10.
On Friday, Johnson's office said the government had followed the rules over the apartment renovation and that the prime minister had not interfered in a government leak inquiry.
In March, Downing Street dismissed as "speculation" suggestions that refurbishments on the flat past year would be paid for by Tory donors through a charity set up for this goal, amid reports that the costs had spiralled out of control.
Asked about the refurbishment plans in March, Johnson's spokeswoman said all donations, gifts and benefits were properly declared and no party funds were being used to pay for the upgrades.
"What I know is the prime minister has personally met the costs of the flat refurbishment and that is what people in Britain want to know", Liz Truss, Britain's trade minister, told BBC television on Sunday.
Donations and loans to political parties of more than £7,500 must be reported to the Electoral Commission, which said it was having "discussions with the Conservative Party", but had not yet launched an investigation.
It also wants a broader independent commission to look into ethics and standards in government after a lobbying scandal involving former leader David Cameron who tried to get ministers to help the now failed finance firm Greensill Capital.
Ministers are now concerned at what he may say when he gives evidence to MPs investigating the government's response to the pandemic next month.