In a recent BBC interview, the politicians argued that the gap between some sports such as rugby union, which has taken significant steps forward regarding concussion, and others like football is far too large.
Headway has long campaigned to raise awareness of inadequate concussion management in sport, at both the professional and amateur level.
"It's simply potluck how safe your sport is in the UK," Tom Watson told the BBC.
"If you're lucky, you play a sport where they take concussion seriously and at a level that provides support, but for far too many people, their sport's governing body is turning a blind eye to the brain injury epidemic and its serious consequences - so we're urging the government to do something about it."
Chris Bryant, MP for Rhondda, added: "Football in particular really has to take this far more seriously.
"There is lots of evidence at the last World Cup that they didn't abide by their own rules. It is still the team's own doctor who's deciding whether somebody should come of the field. It should be, like rugby, an independent person who's making the decision on medical evidence rather than the needs of the team."
Chris Bryant is the chair of the All-Party Parliamentary Committee on Acquired Brain Injury. Headway supports the committee and lent its expertise to its report into concussion, issued last month. The report said there was a "poor awareness" and "lack of knowledge" in managing sports concussions.
Peter McCabe, Chief Executive of Headway, said: “We fully support the comments of Tom Watson and Chris Bryant, and would like to thank them in their efforts to raise awareness on this issue.
“Sport has clear benefits for participants and it is important we encourage people to take part. However, elite-level sport has to set a consistent example for the millions of youngsters around the world who take their lead from their idols.
“A number of sports, especially rugby, have made progress on concussion and its management, but there is still much more that needs to be done.
"Protocols are can only be effective if they are followed, and be seen to be followed. Sadly, as this year’s World Cup shows, this is still not the case.”Back