Campaigners have instructed lawyers to begin a legal challenge over whether leaving the EU means automatic withdrawal from the single market.
The British Influence think tank wants a judicial review of the Government's legal position on membership of the wider European Economic Area which forms the internal trading bloc.
The think-tank believes leaving the EU does not mean quitting the EEA which extends the single market's tariff-free trade in goods to countries like Norway, Iceland and Liechtenstein.
A legal challenge could result in Parliament being given the final say on EEA membership.
A spokesman said: "There is no need for a hard Brexit and there is no mandate for a hard Brexit."
The group believes Britain does not need to quit the single market to control immigration, end payments to EU coffers or return powers to Parliament.
It also says voters did not decide to leave the trading arrangement when they backed Brexit in the June 23 referendum.
Group chairman Peter Wilding said: "This is not stopping Brexit, this is shaping it. The country demands a win-win, smart Brexit, not a lose-lose ideological hard Brexit which will damage the UK, damage Europe and for which there is no need and no mandate."