More than 27,000 people have signed a petition calling for a change to the Highway Code to make junctions safer.
Former Olympic cycling champion Chris Boardman is leading the call by British Cycling to follow the European standard where anyone turning at junctions gives way.
The change would apply to all road users, including cyclists.
Research led by Dr Rachel Aldred, of Westminster University, found the average regular commuting cyclist encounters 25 near-misses each year involving vehicles turning left and right across their path at junctions, of which six are deemed "very scary".
Boardman, whose mother Carol was killed in a crash with a pick-up vehicle while cycling in North Wales last year, said: "We know that the place where walkers - particularly the elderly and parents with children - and those on bikes often feel most vulnerable is when they are crossing junctions.
"Instead of the 14 conflicting rules in an outdated Highway Code, let's borrow the common sense approach used in other European countries to create one simple rule that will make junctions much safer for everyone.
"This wouldn't cost the government money and could be implemented very easily with political will. The cost of doing nothing is far greater."