Brexit is Brexit, and that is what we voted for. Anything else is just a shade of remain. It looks as if the UK is going to take the only viable route to leave, and that is a true Brexit. So what will happen when Britain switches to WTO rules? Well Britain is a member of the WTO in it's own right, and their subscription is paid up to date. The EU is also a member, and it trades with much of the world under WTO rules. When the UK leaves the EU, it will start to trade with the EU under WTO rules. This is automatic, and it is how the system works. The rules also state that the EU has to trade on the same terms as it trades with other non-EU countries.
So the truth is that Britain will continue to trade with the EU, and there will be no disruption. Customs processing will be performed in the same way that Britain checks most of its trade at the moment. Most of its trading is outside the EU anyway.