Some prices will go up so we the british public just end up giving the government more cash via corporate taxation. Less investment will be made in things like advertising in the UK as the budget would be better spent in countries where larger returns can be made on those costs. Staff wages will be under greater scrutiny and so fewer people will be employed and those that remain will be pushed harder.
The end result the british public pay more for things and the government has to use this new tax income to support more unemployed and low income people.
What the british government should be doing is asking how it can make Britain more competitive by reducing complexity in government and therefore reducing the tax burden. If Britain had similar tax rates to the other countries, companies would not have to try moving their income to other countries to maximise their profits.
The only win here is that small businesses who are unable to move money around the world to avoid tax will be on a slightly more even footing with the large corporates if they all have to pay the same tax.