According to reports by Reuters, the draft letter has been signed by around 400 investors.
Bob Blackman, chair of the APPG, is urging the government to step in, ten days before voting closes on the proposed redress scheme for Woodford investors - which could see them receive a maximum of £235m back, representing 77p in the pound.
Registration to vote on Link Fund Solutions' Woodford scheme of arrangement opens
The FCA has urged investors in the former WEIF to back the redress scheme and accept the 77% offer.
But in the draft letter, Blackman accused the regulator of understating investor losses, misrepresenting the value of the redress scheme, acting inappropriately by endorsing the scheme and failing investors by not publishing its investigation into the fund and its former manager.
The APPG chair has also called on City minister Bim Afolami to meet with him and discuss "misconduct and regulatory failures" within the Woodford saga, and to make the case for an independent inquiry later on.
Woodford investors to vote in single class as scheme of arrangement vote delayed
The draft letter stated: "Inevitably [...] the message gets out that the UK financial system is a 'caveat emptor' market in which negligence and dishonesty go unchallenged by a complacent or even complicit regulator, and there is no route to redress for innocent victims."
The final version of the letter may differ from the current draft, however.
If investors vote in favour of the redress scheme, they will not be able to seek further compensation from the Financial Services Compensation Scheme - which can give back up to £85,000 - and will not be able to take further legal action either.
The FCA has been contacted for comment.