The House of Lords has warned that "once-in-a-century" reforms to the global tax system proposed by the Organisation for Economic Co-operation and Development's (OECD) may not be enough to stop multinational companies avoiding billions of pounds in tax payments.

The Lords' economic affairs select committee also recommended increasing funding for HM Revenue & Customs in order to tackle well-funded corporations and allowing politicians to take private testimonies from HMRC officials on tax agreements with companies.

The committee said it was "not clear" whether the OECD reforms unveiled this month ahead of a G20 summit go far enough to stop big companies, such as Amazon, shuffling sales income from British customers to low-tax countries.

"It is not yet clear how effective the proposed solutions will be or whether they can be achieved within the [two-year] timescale," the committee's report, published on Wednesday, said. "In the meantime, the UK faces the prospect of losing much-needed revenue."

The committee urged the Treasury to "urgently review" the UK's corporate tax regime. It also called for a study of the impact of the changes put forward by the OECD, that had been asked to draw up the proposals for a meeting of G20 finance ministers in Moscow.

George Osborne had hailed the OECD tax reforms – potentially the most ambitious internationally-agreed tax changes since the 1920s – as an "important step towards a global tax system that is fair and fit for purpose for the modern economy".

The OECD reforms promise to put a stop to Amazon routing its £4.2bn annual UK sales through Luxembourg, paying negligible UK tax along the way.

Lord MacGregor , chairman of the committee, said: "There is a sense that corporation tax is voluntary for some multinationals… while small UK-based businesses go by the book and have to pay."

He said the government should consider introducing a destination-based cashflow tax, under which companies would be taxed on profits generated in the countries where their customers live.

The report said the public is right to be concerned about "companies paying little or no tax corporation tax in this country". It named and shamed apparent tax-avoidance measures taken by Amazon, Google, Starbucks, Thames Water and Cadbury, before it was absorbed into US group Mondelez.

The committee also raised serious concern that HMRC, the only public body able to see corporate tax returns, has not publicly commented on these cases or the controversial tax deals it reached with Goldman Sachs and Vodafone.

The committee said it was concerned that HMRC may not be "assertive enough" in its tax negotiations with multinationals. The Lords said the government must also give HMRC more cash to enable it to match the financial might of multinationals and their tax advisers. The Treasury pointed out that Osborne recently announced £154m of fresh funding to allow HMRC to draft in an "army of investigators".

The committee also called for the establishment of a joint committee of MPs and peers to take private testimony from HMRC to enable politicians to learn about the difficulties of reaching tax payment agreements whilst not breaching HMRC's confidentiality to taxpayers.

HMRC said: "HMRC officials cannot discuss the details of the tax affairs of identifiable taxpayers – individuals or corporates – except in limited circumstances set out in legislation. Our legal advice is that if Parliament requires HMRC to discuss the tax settlements of named companies a change would be required to the primary legislation governing HMRC."

The Lords committee also called for fresh regulation on tax advisers, which would see them banned from practising if they're caught promoting "blatantly contrived" tax avoidance schemes.