That's just wrong.The idea that the trade we do with Europe is perfectly replaceable with trade to the rest of the world is laughable.
Trade fluctuates all the time, but UK-EU trade has been dropping for several years. Currently, UK-RestofWorld trade is hampered by the fact that we are not allowed to enter trade deals with other (non-EU) countries. With non-EU countries, we either have to trade without a trade deal at all, or we have to trade through EU trade deals. Currently, any non-EU country seeking to trade with the UK is trading with an EU member, and so that country is on the outside of the protectionist barriers that are the EU customs union borders, and so are at a disadvantage compared to trading with the UK once a Brexit was completed.
What is utterly certain is that UK -EU trade will continue, in substantial part, even if we leave. For the reasons why, read that German report on the potential impact of Brexit. Terms will change, and volumes may to a point, but nobody knows, or can know, how much volumes will change or what terms will be until it happens. But it is certain that major EU countries will not just cease exporting to the UK. We are a small country but still a big economy, and doing that would hurt not just the UK but also, for example, Germany and France. Neither side want that.
Trade costs with the EU will perhaps rise, but trade ultimately is determined by consumers. Will UK customers stop buying BMW and Mercedes? Not unless the UK government slaps enormous tariffs on them (despite WTO rules) and the same applies the other way round.
Will there be an effect? Almost certainly. But nobody knows how much because the negotiations have yet to take place.
But just as leaving the EU means the UK would be outside those protectionist barriers when trading into the EU, we and everybody except the EU would be outside when trading with each other. The costs currently incurred by non-EU countries trading with the UK as a result of us being inside those barriers disappear if we are outside, meaning that if EU tariff and non-tariff costs with the EU go up, costs with others go down, for them and us.
It is entirely reasonable to suppose that trade with non-EU countries goes up if the costs of that trade, with the UK, go down. By how much our trade with the EU and others varies remains to be seen, but it is certainly not laughable to see it go up, and very possibly significantly. It's been going up anyway, without being outside the barriers. One reason at least some existing trade is intra-EU is because, currently, we're inside those protectionist barriers.
And by the way, I say this as a UK national that's been living overseas for a very long time, running businesses and that, in the past, looked to the UK for trade but was so put off by the hoops EU paperwork put me through that I gave up and focussed elsewhere.