The Health Secretary said it was “perfectly reasonable” for him to send on a proposal from Brooks Newmark to officials and ask them to examine it.
He said the offer resulted in 90 million protective goggles being provided to NHS workers.
He faced questions on the issue after The Sunday Times secured emails detailing exchanges linked to Mr Hancock, his team and Mr Newmark.
The newspaper reported Mr Newmark, who quit as a government minister in 2014 and stood down as MP for Braintree in 2015 after an internet sex scandal, first emailed Mr Hancock on May 27 last year – some two months into the peak of the first wave.
Mr Newmark attached a detailed proposal explaining he had links to a “well connected and powerful” person in China but that he needed government help in accelerating deals, the newspaper added.
The Sunday Times said Mr Hancock replied: “Thanks. Definitely one for the PPE team who are firing on all cylinders now.”
The newspaper said the Department of Health awarded a £178 million contract for protective goggles to the firm on June 1.
Critics have accused the Government of “cronyism” and giving “VIP treatment” to those with links to the Conservative Party during the pandemic, with emergency powers enabling contracts to be directly awarded rather than through tenders.
Mr Hancock, asked if it was appropriate for Mr Newmark to lobby him, told the BBC’s Andrew Marr Show: “Yes it was absolutely appropriate for people to get in contact with anybody at the Department of Health when the country desperately needed PPE and I sent this contact straight on to the PPE team and they looked at it.
“I don’t have anything to do with the award of contracts.”
Questioned if Mr Newmark received special treatment, Mr Hancock replied: “No, I just pinged it on.”
Mr Marr read out a message from Mr Hancock’s aide to Lord Deighton, the Government’s PPE tsar, in which the proposal was labelled “excellent” and noted that Mr Hancock hoped it could be looked at “urgently”.
Mr Hancock went on: “What I can tell you is that we had a process in place to ensure that when there were opportunities to get hold of PPE, to save lives on the frontline, that they were looked at rapidly – and in this case, we ended up with 90 million goggles for people in the NHS as a result of this approach.”
Told it looked as if those with contacts to ministers received preferential treatment, Mr Hancock replied: “No, that’s not true because this process for making sure that when there were high quality offers that they could be taken up rapidly, that process was open to everybody and many, many people came through that process.
“And the result was that we saved lives on the frontline and at no point did we have a national outage of PPE and I’m incredibly proud of my team that pulled that off.
“But of course when somebody approaches the Health Secretary in the middle of a pandemic when you’re desperately short of PPE, it’s perfectly reasonable for the Health Secretary to send on the email and say can we have a look at this, and then I didn’t have anything to do with the signing of any of these contracts.”
Mr Hancock confirmed he “wanted it to be looked at”, adding: “By the way, 90 million goggles later, I’m glad that I did.
“I sent it, as you can see, and said this is one for the PPE team and that’s the right thing to do.”
Mr Newmark declined to comment to The Sunday Times, with the paper adding sources close to him said he merely helped “chivvy along” an existing process.
Labour deputy leader Angela Rayner said: “It is a recurring theme of the pandemic that ministers have bent over backwards to help their donors, friends and supporters while other companies have had to beg to provide equipment that could help.
“Returning to normal after this crisis is over must not mean a return to Conservative cronyism, deals for mates, and one rule for them and another for the rest of us.”