The Labour leader has already been forced into one U-turn after his initial opposition to increasing corporation tax for big firms faced heavy criticism.
Now, MPs on the left of the party are challenging the front bench to support more radical policies on the economy with a slew of amendments to the government’s finance bill.
Leeds East MP Richard Burgon has tabled two changes to the legislation.
One would mean a new 55% income tax rate on those bringing in more than £200,000 a year. The current highest income tax rate is 45% for those earning above £150,000.
Burgon says more than 300,000 people would be affected by the new rate he proposes, which is estimated to raise up to £1bn per year.
The second amendment calls for a windfall tax on companies who have made “super-profits out of the Covid crisis”, which the MP says mirrors Gordon Brown policies on “the excess profits of the privatised utilities” in 1997.
Burgon’s amendments to the finance bill call on the government to provide reports into these alternative tax policies and the revenues they would make for the Treasury.
Former shadow chancellor John McDonnell has also tabled a number of amendments, including one that would wreck Sunak’s plan to freeze tax thresholds and drag more of the low-paid into paying more income tax.
A Labour left source told HuffPost UK: “The public supports higher taxes on wealth and companies, and we need to be leading that argument.
“Biden is talking about big tax rises to rebuild infrastructure and we should be doing the same. It’s frustrating that we aren’t.
“With people facing the deepest crisis in decades, Labour needs to be taking the gloves off in the fight against the Tories and showing how we will build a fairer country.”
Although the amendments are unlikely to win widespread backing across the Parliamentary Labour Party, the moves underline disquiet among Starmer’s ranks over the leader’s strategy after a year in the job.
Starmer and his shadow chancellor Anneliese Dodds have set out few policies, underlining that the next general election may be more than three years away.
But many within the party are impatient and called for a special conference earlier this year.
Burgon, whose wealth tax proposals have the backing of the Socialist Campaign Group of MPs, said: “This pandemic has shone a spotlight on the deep inequalities that run through our society.
“Keeping taxes low for the very rich does not boost the economy – it just lets inequality run out of control
“A more progressive tax system could make a progressive real difference in building a more equal, inclusive society. As we come out of this pandemic we need to be looking at more progressive income taxes, one-off wealth taxes and taxes on those companies that have made super-profits from this crisis.”
HuffPost UK has contacted the party for official comment.
This article originally appeared on HuffPost UK and has been updated.