The organisation's policy and legal affairs director, Martin Gibbs, says too many cyclists are being caught up in serious incidents on the road and that British Cycling's members expect them to take a lead in improving their safety.
“The Government are keen to see more cyclists on the road and we've been extremely successful in achieving that, but we also have a responsibility to make sure that the roads are as safe as they can be," Gibbs said.
"We're undertaking a survey of our members to find out what they regard to be the most important road safety issues and we'll be taking that information to engage with the Government to seek the necessary changes in legislation.
"There are many issues at play here, such as increasing the level of awareness of cyclists, increasing mutual respect, improving road design and layout, and looking at how we can communicate the responsibility that drivers have towards cyclists and pedestrians.
"I think that too often the courts get sentencing wrong when a driver causes injury and we need to look at the content of the driving test and issues like blindspots on lorries and cars."
He added: "Our thoughts are with Simon and his family, and we have of course been in contact to offer our full support as he's been a member of ours and a superb athlete for many years".
Richardson remains in a critical but stable condition following the crash near Bridgend, Wales. He suffered double fractures to his spine and pelvis, a broken sternum and lacerations to his left leg. Surgeons decided not to operate immediately, but haven't ruled it out.
No injuries were sustained to his right leg – the one he uses to power his bike. A man arrested following the incident, who hasn’t been named, has been bailed to return to Bridgend police station on 13 October.