British Cycling director Martin Gibbs told BBC Sport: "[Shane's] had a severe knock but he should be fine."
Following the incidents, British Cycling has called on the government "to put cycling at the heart of transport policy to ensure cycle safety".
Gibbs said: "These incidents do remind you that we've got a long way to go. We need to look to our cousins abroad and [Denmark capital] Copenhagen and see what they've done.
"Around 30% of people making journeys there do so on their bike. We need the Department for Transport to stop thinking of cycling as an add-on."
Tour winner Wiggins' Olympic golds
Former British time trial cyclist Michael Hutchinson, who now works as a journalist for Cycling Weekly, says changes are needed to the driving test to increase safety on the roads for cyclists.
He told the BBC: "There have been suggestions that perhaps the driving test could include not only more instruction on cyclists but perhaps even a cycling module where new drivers have to pass a cycling test before they're allowed to drive a car.
"It would help people realise the danger that cyclists are in and the vulnerability that a lot of people I think don't realise."
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