The mainstream British approach has always been that European issues should be intergovernmental, not supranational. However British politicians have been foolish enough to believe that these issues could be intergovernmental within the context of an organisation that was always on the glidepath to a superstate from its very inception.
As it is, EFTA membership is probably the only way of breaking the impasse, of respecting the result of the referendum after three wasted years with the country in limbo, whilst delivering a compromise. The Republic of Ireland was also a member of EFTA and like Denmark only joined the EEC at the same time as the UK to keep its main agricultural export market.