Cyclists may win priority over cars on scores of urban roads, with motorists restricted to 15mph (24km an hour) and handed three penalty points and a fixed penalty £100 fine if they overtake bikes, according to a government proposal. .

However, cars will still dominate most streets: the policy would only cover some cities and "lightly trafficked roads where cycle flows are high".

The proposal for "cycle streets", backed by roads minister Robert Goodwill, is one of many changes and improvements suggested in a Department for Transport consultation document on making streets safer, through measures including reformed traffic regulations and signage.

The document says the bike priority streets will be tested in cities that have made a commitment to promoting cycling – and to taking any available government cash for the purpose – including London, Manchester, Birmingham, Newcastle upon Tyne and Oxford.

"This is a bold initiative, which is being considered by some of the Cycle Cities and London, possibly including a ban on overtaking on lightly trafficked roads where cycle flows are high. Subject to any scheme trial, this prohibition could be accompanied by an advisory speed limit of 15mph," it says. The consultation ends in June.

The British Cycling association has welcomed the proposed changes, but warned political determination and funding were essential to make them work.

"We still need the leadership to ensure these designs make it on to our roads, a national commitment to grow cycling levels, and it must be backed by a long-term budget line. Only then can we say that the prime minister's ambition of creating a 'cycling revolution' can be achieved," it said.