The warning came as the PIA admitted that out of almost 400,000 so-called priority cases which should have been dealt with by the end of last year, just 7,000 investors have been offered redress.
About 6,000 of those offers came from independent financial advisers. Big insurers, banks and building societies who have 270,000 priority cases between them, had only offered redress in 1,000 instances.
Joe Palmer, chairman of the PIA, said yesterday: "[We] will not allow the situation to drift. Firms which are found not to be devoting sufficient time and resources to the review will be disciplined. The penalties will match their failure.
"We know that there have been delays to the review process which are outside our control. But it is clear that progress is not as good in some cases as it should be."
A PIA spokesman added that likely disciplinary action included fines, or even suspension from trading where necessary.
Mr Palmer's comments follow the first reports to the PIA by members of the progress reached in the pension transfer review at the end of December last year. The review, initially ordered by the Securities and Investments Board, followed an investigation which showed that up to 1.5 million people might have been mis-sold a pension.
The reports show that of nearly 1.1 million cases so far indentified as requiring investigation, more than 390,000 are classed as priorities, higher than original estimates.
As well as insurers, big banks and building societies contributed more than 60,000 of those cases, compared with 16,000 from large independent financial advice firms with a national network of offices, and 43,000 from small IFAs.
The PIA set 31 December last year as the target date by which the vast majority of priority cases, then thought to number about 350,000, had to be reviewed.
Among cases deemed urgent are those where a pension plan holder is dead or close to retirement, or where a person was wrongly advised to opt out of an occupational scheme while still in that company's employment.
Despite the regulator's hopes, the review became rapidly bogged down in a series of lengthy delays, caused by legal action, computer problems and threats by specialist insurers to invalidate the cover of advisers who sent out letters referring to compensation.
Separately, the Investors Compensation Scheme, the safety net for victims of fraud and bad advice, declared seven investment firms in default which could trigger potential compensations claims worth millions of pounds.
The claims expected are the first to be linked to the pension transfer scandal. The companies affected are: Cameron Law & Co, in Birmingham; Du Bara Investments, in Carmarthen, Dyfed; Homer MacKenzie, in Milton Keynes; Individual Savings & Insurance Services, in Reigate; Langley Financial Planning, in Langley, Berkshire; Scott & Scott Financial Services in Edinburgh; Stephen Welsh & Co, in Plymouth.Reuse content