The Labour MP, who also welcomed the government’s move to lift all remaining travel restrictions, described curbs implemented throughout the past two years as "draconian".
"I’m delighted that England is following Norway, Ireland, Hungary and several other countries in lifting all remaining travel restrictions," Bradshaw told the House of Commons.
"But can the secretary of state [Grant Shapps] assure me that the public inquiry into Covid, when it happens, will have full access to all of the various and quite secretive committees that the government relied on when it imposed those travel restrictions.
"Many of us believe, and the growing evidence suggests that, for countries like ours, which was never going to have a zero-Covid strategy, those draconian travel restrictions did more harm than good."
In response, transport secretary Grant Shapps said the inquiry is there to "learn the lessons about Covid".
"I think it’s incredibly important that it does, not just obviously with relation to travel, but across the entire plethora of everything that happened during Covid," he continued.
"Of course we want to learn the lessons; without learning the lessons of the past, we can never improve things for the future."
Meanwhile, Transport Select Committee chair Huw Merriman urged Shapps to ensure Border Force’s resources are ramped up in line with the projected increase in airport footfall this summer.
"Can [Shapps] do everything in his power, working with the home secretary, to ensure we have everybody at the airports we need," he continued.
"I used the airport at the weekend and they were fantastic. It was really efficient, but as numbers upscale, so must they."
In response, Shapps said he would liaise with home secretary Priti Patel to ensure Border Force is allocated the provisions needed to scale up its operations as airports get busier.
"Border Force, and making sure the resources are in the right place, are going to be very important, particularly as our airports get busier once again," Shapps added.
