Labour has said there are “serious questions to answer” after it was revealed that Health Secretary Matt Hancock has shares in a family company which has contracts with the NHS.

Mr Hancock declared in the MPs’ register of interests in March of this year that he now owns shares in Topwood Limited, which specialises in secure storage, shredding and scanning of documents.

The Health Service Journal (HSJ) reported that the firm, in which his sister owns a larger portion of shares, won a place on a framework to provide services to the English NHS in 2019, as well as contracts with the NHS in Wales.

It also reported that the Health Secretary did not declare his connection to the company in the relevant register of interests, a claim which has been rejected by the Government.

A Government spokeswoman said Mr Hancock had acted “entirely properly in these circumstances” and that all declarations of interest have been made “in accordance with the ministerial code”.

Asked if the Boris Johnson still had full confidence in Mr Hancock, a No 10 spokesman said: “Yes.”

Meanwhile, a Whitehall source said the Health Secretary has no active participation in running Topwood Limited and that neither he nor the Department of Health and Social Care (DHSC) were involved in awarding the contracts.

The source said Mr Hancock had discussed with the department’s top civil servant, the Permanent Secretary, that he was to be given the shares in the firm before accepting them.

At this point it was decided that, if any conflicts of interest did arise, they could be dealt with in line with the ministerial code, which sets out standards of conduct for ministers.

Mr Hancock has no responsibility for NHS Wales, which reportedly awarded the firm £300,000 worth of contracts, as health is a devolved matter and so dealt with by the Welsh Government.

It follows accusations of “cronyism” within Government by Labour, which is calling for a full inquiry into the Greensill Capital lobbying controversy.

Shadow health minister Justin Madders said: “It is now clear this Conservative Government has been infected with widespread cronyism and is unable to identify where the line is drawn between personal and departmental interests.

“It’s one rule for them, another for everybody else.

“There are serious questions to answer from Matt Hancock and there needs to be a full inquiry and immediate publication of all documents relating to Topwood’s acceptance on to the framework contract in 2019.”

Speaking on a Holyrood election campaign visit to Scotland, Labour leader Sir Keir Starmer told the PA news agency: “We need to get to the bottom of this, we cannot have this situation where there’s apparent double jobbing.

“If these were one-offs, that would be one thing, but at the moment we are getting drip, drip every day more evidence of cronyism and of the return to sleaze in government.

“That is why we the Labour Party are calling for a full and transparent inquiry that can get to the bottom of this so we can have stronger laws in place but make no mistake this is the return to Tory sleaze.

“We’re not going to give up on the argument there needs to be a full inquiry into this. The Prime Minister is setting up a very narrow inquiry with a government appointee from a law firm that actually lobbied to loosen the lobbying laws, you couldn’t make it up.

“We need this wider review, this wider inquiry. The Government shouldn’t have blocked that last week. If they are saying ‘we want to get to the bottom of it’ then let them get to the bottom of it, so support the call for this independent inquiry.”

Labour deputy leader Angela Rayner said it “appears that the Health Secretary has breached the ministerial code” and demanded that he explain why he failed to declare that his sister is a director of the company.

She said: “It is clear that Tory sleaze and cronyism has engulfed this Government, making it even more urgent that the Government publish the delayed register of ministers’ interests in full immediately.

“Given it was the Health Secretary who was found by the courts to have acted unlawfully on contract transparency, with this latest scandal the public will rightly expect the utmost transparency.”

William Wragg, who is chairman of the Commons Public Administration and Constitutional Affairs Committee, said there are questions about whether the register was updated with details of Mr Hancock’s sister.

“I think his record, from his personal point of view, is up to date. I think the question is, was his register updated with that of his sibling?” the Conservative MP told Times Radio.

The committee announced on Thursday that it would be carrying out an inquiry into lobbying and business appointments issues that have come to light since the Greensill row.

A Government spokeswoman said: “Mr Hancock has acted entirely properly in these circumstances. All declarations of interest have been made in accordance with the ministerial code.

“Ministers have no involvement in the awarding of these contracts, and no conflict of interest arises.”