The Office for National Statistics said it played a role in reducing inflation in 2023, and it appeared popular.
An evaluation of the first ten months - not published until 2025 - found that the scheme did contribute 5% of the 13% rise in bus usage during that period. Lower-income passengers felt the most financial benefit.
However it did not score highly when it comes to value for money. How much money people saved varied depending how much fares in their local area cost before the cap.
In those first ten months, £210m was spent on the scheme, less than the £245m budget.
Sir Keir's government allocated £150m to fund its £3 cap for 2025.
The Burnham government points out going back to a £2 cap should particularly help passengers in rural and coastal areas, where single fares can be higher.
The new cap will take effect from 1 January 2027 for fares on participating buses outside of London.
Shadow Chancellor Mel Stride said the government has not actually specified where the money will come from to fund the bus fare cap extension.
"That is a worrying sign, we need to have a government which is on top of the public finances, not one that is making lots of spending commitments without explaining where the money is going to come from," Stride told BBC Breakfast.
In its announcement, the government said £454 million will be reallocated from the Department for Energy Security and Net Zero.
It says this will be used in addition to funds already earmarked by the Department for Transport for buses.
It is the second day in a row that the new prime minister has announced cost saving measures, following Tuesday's VAT cut on household electricity bills later this year.
But his plan to pay for the policy by scrapping Sir Keir's digital ID scheme led to an early row over whether the plan was properly funded.
In his first cabinet meeting on Tuesday, Burnham promised to lead a "cost of living government", telling ministers that he wanted to give people a "sense that help is coming" on costs.