HM Revenue and Customs must rethink its plans to share millions of people's personal tax data with private companies and researchers, a prominent Lib Dem MP and privacy campaigners have said – as they handed in a petition of 300,000 signatures to the government.

Julian Huppert, a Lib Dem member of the Commons home affairs committee, said HMRC would "seriously undermine the confidentiality we expect" if it proceeded with the proposal to relax restrictions on sharing taxpayer data and potentially selling it to private firms.

Although the data would be anonymised, critics fear it could include details about income, tax arrangements and payment history and carry a risk that people could be identified. The campaign groups 38 Degrees, Open Rights Group and Sum of Us handed in a petition calling for an end to the plans.

Last month, the Guardian revealed that HMRC was considering sharing anonymised tax data with third parties including companies, researchers and public bodies. The campaign groups are concerned that everyone is forced to give HMRC personal information but is it is very difficult to give or withdraw consent about what happens to that data.

Huppert said: "Personal data can be very revealing, showing off a huge amount about who we are and what we do. HMRC should rethink their plans to sell this data off to private companies. People don't have choice when it comes to sharing personal data with the tax office but they should be able to refuse to have it shared with other companies or public bodies. HMRC's proposals could seriously undermine the confidentiality we expect."

Jim Killock, executive director of Open Rights Group, said: "The government may claim that it will be anonymous but it's impossible to guarantee that data won't be re-identifiable. We have a right to know how the government is going to use our data and who it wants to share it with."

The plans have previously been criticised by the Tory MP David Davis, a former minister and shadow home secretary, who described the proposal as "borderline insane".

HMRC has said it is "committed to protecting its customers' information". A spokesman said: "We shall be consulting further on implementing the proposals for sharing anonymised data, and would only take forward specific measures where there was a clear public benefit and subject to suitable safeguards."