It follows claims that in the first phase of tram works starting in 2009, 74 cyclists suffered falls on Princes Street as a direct result of the works.
It is also claimed a number of recommendations were put to the council in a bid to reduce cyclists' injuries but only a handful have been implemented.
Sara Reed, an experienced cyclist from Edinburgh, was recently injured as a direct result of the works in the city.
She sustained a broken collar bone and other injuries when her bike got stuck between the metal tram lines.
Ms Reed said: "Edinburgh City Council knows many cyclists are having accidents as a direct result of the tram tracks and have taken no action.
"I have commuted to work by bike for 20 years and have never experienced a danger like this in the city. Edinburgh is no longer safe for cyclists.
"People are getting seriously injured and the council needs to resolve the situation before someone is killed."
Thompsons Solicitors is acting for a number of people who have suffered injury or damage as a result of the tram lines in Edinburgh
Partner Patrick McGuire said: "The situation in and around Princes Street is a fatality waiting to happen."
UK charity Cyclists Defence Fund is working alongside the legal firm to put pressure on the council to improve safety in the city. Chairman Chris Field said: "Local cycle campaigners had repeatedly voiced concerns about the hazards of Edinburgh's tram scheme."
A council spokesman said: "It's a priority to improve safety right across the city and the council's coalition agreement commitment to invest 5% of the transport budget on provision for cyclists will help achieve this. We lead a cycle forum but we're always happy to listen to new suggestions."