The Labour peer at the centre of a row over donations to Sir Keir Starmer is under investigation by the Lords’ standards watchdog over an alleged failure to register interests.

Lord Waheed Alli is facing a probe over potential breaches of parliamentary rules surrounding openness and accountability in the members’ code of conduct.

A Labour spokesman said: “Lord Alli will co-operate fully with the Lords’ Commissioner and he is confident all interests have been registered. We cannot comment further while this is ongoing.”

It comes after a backlash over Sir Keir and other Cabinet members – who vowed to “clean up” British politics – accepting tens of thousands of pounds worth of gifts and freebies, many from the long-standing Labour donor.

The Prime Minister has since committed to overhauling hospitality rules for ministers to ensure better transparency about what is provided.

Lord Alli, a media tycoon known known in political circles for years, was brought to wider public attention in recent weeks due to scrutiny of his gifts to the Prime Minister.

These included £20,000 in accommodation during the election campaign, which the PM said was to allow his son to study for his GCSEs in peace at the peer’s central London flat while the family home was surrounded by media.

The Prime Minister also accepted glasses and clothing for both himself and his wife Lady Victoria Starmer, declaring £16,000 in donations and £39,122 in gifts from the peer since October, according to the latest register of interests.

Sir Keir has argued Lord Alli, who entered the spotlight after it emerged in August that he had been granted a temporary Downing Street security pass after the election without having a Government role, was motivated to help financially because he wanted Labour to win the election.

But the controversy overshadowed the party’s first annual conference since entering Government and was cited by Canterbury MP Rosie Duffield as one of the reasons she resigned the whip last week in protest against the leadership.

According to an update published on Parliament’s website on Wednesday, Lord Alli is being investigated by the Lords’ commissioner for “alleged non-registration of interests leading to potential breaches of paragraphs 14(a) and 17 of the 13th edition of the code of conduct”.

These rules relate to making clear what the interests are that might be reasonably thought to influence a member’s parliamentary actions and ensuring entries are up to date.

The allegations are understood to relate to a clerical element of already-declared interests, rather than connected to his donations.

The SNP called for a “full investigation” by the standards commissioner and the independent adviser on ministers’ interests into donations made by Lord Alli to Labour MPs as well as the “narrow inquiry” announced on Wednesday.

The party’s Cabinet Office spokesman Brendan O’Hara MP said: “The Labour Party freebies scandal has wrecked public confidence in Keir Starmer, his Government and the Westminster system, and there must be full transparency and accountability.”

He added: “We need answers – including why these gifts were taken, whether there have been breaches of the MPs’ and ministerial code, and why Lord Alli was handed a security pass to the halls of power.”