The UK does a huge bulk of their trade with the rest of Europe and very little with Australia, etc. Tariffs aren't that much of a barrier when companies and individuals want to import things you really want from other countries, so I don't think leaving will increase it that much with other countries.
There are serious structural problems in the UK that weren't solved before that weren't caused by the EU, namely the lack of good jobs (the UK has excelled in creating shitty low paid jobs, mostly), chronic underinvestment and too many people are in poverty, have bad living standards and just barely live on from day to day. The EU didn't have much impact on the policies of the government, because the UK could always make their own laws and has always been sovereign. In fact the EU has dumped money into the poorer regions of the country. Funding that will go if we go through with this nonsense.
I hope we stay in the single market, get some token restrictions on free movement like no benefits at all for 5 years for a non-citizen like Germany, you can only live here for 3 months without a job (it was always the case, you can pretend it's something new given how uninformed a lot of people are about the issue) has recently done, so you can satisfy the mandate, look towards the future instead of to the past , as May herself has said and not make the economy take an unnecessary hit.