More than 1,000 have signed a letter to Mr Cameron which says the referendum result is “advisory” and not legally binding.
They say primary legislation will be needed before Article 50 of the Lisbon Treaty - the route via which members states leave the EU - can be triggered.
The lawyers say the Government should organise an independent investigation into the pros and cons of withdrawal before making exit plans.
They say their letter will reach Mr Cameron this week and proposes a way forward which “reconciles the legal, constitutional and political issues” triggered by the Brexit vote.
Philip Kolvin QC, who co-ordinated the creation of the letter, said: “Parliament is sovereign and the guardian of our democracy.
“MPs are elected to exercise their best judgment on the basis of objective evidence, to safeguard the interests of the country and their constituents for this and future generations.
“At this time of profound constitutional, political and possibly social and economic crisis, we look to them to fulfil the responsibility placed upon them.”
One barrister involved, Aidan O’Neill a constitutional and EU law specialist, said: “The Brexit referendum has made clear that the UK is not a united nation-state, but a divided state of nations.
“But it has given no mandate or guidance as to what our nations’ future relationship might be with Europe, and with each other.”
He added: “Precipitate or unilateral action by the UK Government to trigger Article 50 will simply further divide us.”