If we leave the EU in the manner which the government is currently proposing, cutting all ties and erecting barriers to trade, the only way the UK could compete on the world stage is by becoming a tax haven with low levels of corporation tax and low levels of personal tax on the wealthy. In such a scenario the inevtiable result is that public services would be cut to the bone or privatised, with the current high EU standards on safety and environmental standards being sacrificed in order to allow businesses to make greater profits.
So if we go through with a complete divorce from the EU, what then for the UK? We've erected huge barriers to trade and movement between the UK and the rest of the EU; barriers that some intend as preventing investment and employment from leaving the UK but which also have the unfortunate result of preventing investment from coming into the UK and diverting it elsewhere. How can we still compete on the global stage in such an scenario?
The answer is found in Theresa May's Lancaster House speech of 17th January 2017 when she talked of "being free to change Britain's economic model". During the referendum campaign other Conservative politicians such as Priti Patel and Michael Gove talked of "EU red tape" but were conspicuouslay careful to avoid specifying exactly what "red tape" (or EU laws) they objected to. The answer is that they, and indeed all of the right wing of the Tory party, object to the EU's laws on the likes of workers rights and environmental standards. They interpret these as a burden on businesses and the ability to make profits. Gove has talked again about "slashing EU standards" on matters as diverse as wildlife protection and drugs safety whilst fellow Leave supporter Jacob Rees-Mogg has said that Britain could cut standards "a very long way" and that standards "good enough for India" could be good enough for the UK. One other argument put forward by the Leave side was for cheaper food after leaving the EU - aside from the fact that we import over half our food (and much of that food is currently sourced from the EU and is tariff-free), if we axe tariffs on food imports from some countries, we have to do the same for all countries (because of World Trade Organisation rules), the standards for food would drop if we left the EU. The EU currently enforces high standards both of food safety and quality but also of related matters such as animal welfare and creating a competitive EU-wide market for agricultural produce. These standards apply whether the produce is grown inside the EU or imported into the EU (see also: laws not made in this country, sovereignty issues in general) and would therefore apply to us if we chose to leave the EU but still wanted to export agricultural produce to the remainder of the EU (two thirds of our farming food output is currently exported to the EU).
Taken together, the logical conclusion of leaving the EU is that either we leave effectively in name only, continuing to abide by EU regulations and rules but without having our current say in how these are made or we leave completely and erect barriers between ourselves and the rest of the EU. This later scenario is what the Euro-phobic right wing of the Conservative party, currently emboldened by the referendum result, wants and sees as within its grasp. The only way in which the UK (presuming the UK remains intact in such a scenario) could remain competitive with such barriers in place would be to slash taxes - especially corporation tax - and to dismantle standards such as workers' rights (to paid annual leave, maternity leave, sickness pay), animal welfare standards, food safety standards and environmental protection laws. We would have to become a "bargain basement" economy with all costs (especially costs that don't yield a direct financial return, such as environmental standards and workers' rights) cut as far as possible. Such an economy would have much reduced general taxation income and so public services would also have to be cut or privatised in order to balance the state's books: you already have to pay for a doctor's appointment in Jersey and such a system could well spread to the mainland UK if we leave the EU in the most extreme manner, cutting all ties and erecting barriers to trade.
This is also what Nigel Farage secretly wants: an economy in which the tax affairs of he and his wealthy friends are not examined too closely and leaving the rest of the population to either pay more taxes or to suffer from public service cuts.