Mr Woodford’s flagship fund was wound up in 2019 leaving small investors with big losses.
Campaigners said 300,000 people had been left “scrabbling to make ends meet” by the collapse.
Mr Woodford has said the fund could have recovered if not forced to close.
Activists Gina Miller and Alan Miller, co-founders of the True and Fair Campaign, which seeks improvements to consumer protection standards, wrote to the Treasury Select Committee on Tuesday urging an independent investigation.
“We believe it ought to be a very serious source of public policy concern that high profile individuals such as Mr Woodford can be allowed to recommence trading, with the slate ostensibly wiped clean, when over 300,000 people some of whom may be your own constituents, are scrabbling to make ends meet after seeing their life savings decimated and their prudent actions and hopes for a secure and comfortable future suddenly and unexpectedly dashed,” the activists said in a letter.
Mr Woodford built his reputation as a star stock picker over 26 years at the City firm Invesco. An investment of £1,000 in his first funds would have returned £25,000 by the time he left.
But after he set up his own business, several investments turned sour, causing the value of his funds to plummet and investors – most of them not professionals – to pull out millions.
As a result, his flagship Woodford Equity Income Fund was first suspended, then shut down, with Mr Woodford removed as investment manager in October 2019.
He then said he would resign from his other remaining funds and wind down his investment company, Woodford Investment Management.
Speaking publicly about what happened for the first time since 2019, Mr Woodford told the Sunday Telegraph recently: “I’m very sorry for what I did wrong. What I was responsible for was two years of underperformance – I was the fund manager, the investment strategy was mine, I owned it and it delivered a period of underperformance.”
Equity income funds are normally bought into by amateurs who ask a fund manager to invest in different businesses for them.
But from reportedly being worth £10.2bn in May 2017, the fund struggled to plug holes as investors pulled out around £10m every day.
By the time it was suspended, the Woodford fund was worth £3.7bn.
Mr Woodford said he warned administrator Link Fund Solutions against closing the fund and said had investors stuck with him they would be “enjoying the fruits of that faith”.
Saying he was “very sorry for what I did wrong”, he added: “I can’t be sorry for the things I didn’t do. I didn’t make the decision to suspend the fund, I didn’t make the decision to liquidate the fund. As history will now show, those decisions were incredibly damaging to investors and they were not mine.”
Link Fund Solutions was approached for comment.
Mr Woodford’s new investment firm, called Woodford Capital Management Partners (WCM), will be based in Buckinghamshire and Jersey.
It will work with Acacia Research, a US investment company, to advise on a portfolio of life sciences company holdings. Acacia bought the portfolio from the Woodford Equity Income Fund’s administrators after it shut down.
Mrs Miller said the move “discredit[s] both the regulator, and the entire UK financial services sector at a time when trust in the sector has rarely been more crucial”.
“The British public deserve much better,” she wrote in the letter.She and Mr Miller also called for parliament to examine the role of the Financial Conduct Authority (FCA) in supervising Mr Woodford.
The events leading up to the fund’s collapse in October 2019 are still being investigated by the UK watchdog.
Mark Steward, the FCA’s director of enforcement and market oversight, said: “I recognise the time taken to investigate causes frustration among those affected by a firm or fund failure and who are, understandably, looking for answers.”
The watchdog’s investigation had been hampered by not having access to certain documents and witnesses during the coronavirus pandemic, and Mr Steward said the investigation was “complex”.
He added that any regulated firm needed to comply with standards including “the sustainability of the firm’s business model and the fitness of its management.”
The FCA and its Jersey counterpart would share information about Mr Woodford’s new venture, he said.
He added that the FCA would not prejudge the outcome of an investigation.
Neil Woodford’s return ‘is a kick in the guts’
Others have said caution is warranted.
“Should Woodford be allowed to open a new fund to professional investors? Particularly as they might not know what risks they are taking on? I think not,” said Paul Resnik, chief ethics officer of the Suitable Advice Institute, an investment advice company.
“We need to see the result of the Financial Conduct Authority’s analysis and the outcomes of impending court cases and class actions first,” he said