There is no reason why the British government can’t proceed with Brexit while maintaining access to the single market. This will of course necessitate the free movement of peoples through Europe. This option is often called the Norwegian model.
There is a great deal of frustration and anger from Remainers and particularly from the voting youth due to the perception that the leave voters, voted out ‘solely’ due to a desire to see controlled immigration. The Norwegian model would be a fantastic way to put this theory to the test. Allowing the free movement of peoples to continue, allowing trade to continue, but dispensing with the undemocratic institutions.
The British government could decide which EU legislation should be discarded and which should be amended in the British interest. If we proceed with this approach Article 50 will not be worth the paper it will be written on and much of the legitimate Scottish and Irish nationalist concerns will be mitigated.