The Prince of Wales's estate should be investigated following claims that it is exploiting an "unfair advantage" over commercial rivals because it is exempt from business taxes, a committee of MPs will say on Tuesday.

The public accounts committee is to urge the Treasury to assess whether the Duchy of Cornwall is competing on an "unlevel playing field" because it is not liable for corporation tax or capital gains tax. The move follows a series of claims, first reported in the Guardian, that the duchy – which manages a portfolio of land, property and investments – is running a "well entrenched tax avoidance scheme".

MPs accused the Treasury of failing to properly scrutinise the duchy's finances because it relies on estate officials to provide it with accurate information and does not carry out independent checks.

The committee's chair, the Labour MP Margaret Hodge, said: "Details of the treasury's approvals for the duchy's proposed land transactions over £500,000 – of which there are around 15 a year – are not published. Greater transparency is needed. The duchy enjoys an exemption from paying tax even though it engages in a range of commercial activities. This tax exemption may give it an unfair advantage over its competitors who do pay corporation and capital gains tax. The treasury should examine whether the duchy's tax exemption creates an unlevel playing field."

The duchy owns large tracts of rural and commercial property as well as housing in the south-west of England. Among its assets are a Waitrose supermarket depot in Milton Keynes and a Holiday Inn hotel in Cornwall. In the last financial year the duchy generated £28.8m and the prince received an income of £19m – up 4% on the previous year. The money is partly used to fund his and his family's public, charitable and official duties and the prince voluntarily pays income tax on the cash left after costs, around £9.2m last year, the committee said.

Only the royal family, its advisers and HM Revenue and Customs currently know what the prince claims as his expenses before tax on his £19m income from the Duchy of Cornwall.

The MPs called for his income tax arrangements to be opened up to scrutiny to improve transparency. It said the combined income tax and VAT paid by the prince was £4.4m, but how this was broken down was unknown.

A Treasury spokesman said: "The Treasury has a constructive working relationship with the Duchy, and challenges decisions where appropriate."

A Duchy of Cornwall spokeswoman denied there was a tax advantage over competitors. "The Duke of Cornwall's income is taxed at income tax rates. The duchy is not subject to corporation tax and the duchy is not a corporation. The duchy is exempt from tax on capital gains, any capital gains have to be reinvested in the business and cannot be distributed."