Roberto Coladangelo was confirmed as the brother of Gina Coladangelo on Saturday, who made headlines after she was spotted kissing Mr Hancock in his office.
Mr Coladangelo works as the strategy director of Partnering Health Limited (PHL Group), which provides urgent and primary care services.
On Saturday a spokesperson for PHL said its contracts had always been awarded in the correct way by the Department of Health and Social Care (DHSC).
They said: “PHL has been operating for over 11 years and at all times has secured contracts through the robust tender and procurement processes put in place by local Clinical Commissioning Groups (CCGs).
“At no time have any contracts been awarded outside of these rigorous processes and no contracts have ever been awarded by the Department of Health and Social Care.”
There is no suggestion of any wrongdoing in regard to the awarding of any contracts to PHL.
Mrs Coladangelo, who is married to the founder of the retailer Oliver Bonas, Oliver Tress, has been a friend of Mr Hancock since they met at Oxford University and was appointed to the DHSC last year.
She was initially taken on as an unpaid adviser on a six-month contract in March 2020, before being appointed as a non-executive director at the department.
On Friday, CCTV images published by The Sun showed Mrs Coladangelo and Mr Hancock kissing in a Department of Health office in early May when Covid-19 guidance was that people should remain socially distanced from people from outside their home.
He said: “I accept that I breached the social distancing guidance in these circumstances, I have let people down and am very sorry,” he said.
“I remain focused on working to get the country out of this pandemic, and would be grateful for privacy for my family on this personal matter.”
It comes as Mr Hancock’s job hangs in the balance after he was ruled to have committed a “minor” but unintentional breach of the ministerial code by failing to declare that a family firm in which he held shares won an NHS contract, following a probe by the Prime Minister’s ethics adviser.
Independent adviser on ministerial standards Lord Geidt found that Mr Hancock, 42, should have declared that Topwood Limited, a firm owned by his sister and in which he held 20 per cent shares, was approved as an NHS contractor.
Lord Geidt did not recommend that he resign.
In February, Mr Hancock was also forced to defend his connection to Hinpack, a manufacturing business run by former publican Alex Bourne.
The Guardian reported at the time that Mr Bourne, who used to run the Cock Inn in Little Thurlow, a village in the Health Secretary’s West Suffolk constituency, contacted Mr Hancock over WhatsApp to offer his services during the pandemic.
The firm partnered with a diagnostics supplier to produce specimen collection tubes and funnels for Covid-19 testing but Mr Hancock and Mr Bourne both said the Health Secretary had not been involved in awarding the contract and told Mr Bourne to apply through the Government website like everyone else.