One interesting proposal for Britain's future relationship in a post-Brexit world has been the idea of a 'Continental Partnership' put forward by a group of six senior policy makers and scholars and published by the Brussels think tank Bruegel: Continental Partnership
They 'propose a new form of collaboration, a continental partnership. The UK will want to have some control over labour mobility, as well as leaving behind the EU’s supranational decision-making. The proposed continental partnership would consist in participating in goods, services, capital mobility and some temporary labour mobility as well as in a new system of inter-governmental decision making and enforcement of common rules to protect the homogeneity of the deeply integrated market. The UK would have a say on EU policies but ultimate formal authority would remain with the EU. This results in a Europe with an inner circle, the EU, with deep and political integration, and an outer circle with less integration.'
Britain would continue to pay into the EU budget which would allow it access to key areas of the single market. The blueprint would leave the UK free to impose quotas on EU workers, so addressing one of the key concerns of Brexiteers, but Britain would have to make major concessions in other areas. The acceptance of case law from the ECJ would be particularly difficult for Leave supporters to swallow.
However, the UK would have a voice on matters affecting its shared market with the EU which would go beyond the consultation currently offered to Switzerland and Norway.