Close to. I mean, the UK already has lower corporate tax rate than a lot of countries. Japan has a 38% corporate tax rate, for example, so why hasn't Nintendo moved to London? Because Japan is where the staff and infrastructure are. Companies have many, many reasons for the precise location of their headquarters, and corporate tax rate is only a small component. So large changes in corporation tax only prompt small changes in corporate location.
Consider my small economy where all the firms together make £1000 and I tax at 10%. I decide to reduce my tax rate to 9% to get some of the firms in your economy to leave, because frankly Cyclops I'm amazed you had a personal economy in the first place. For my decision to bring a net revenue increase, I need 0.09*(1000+F) > 0.1*1000, which solves for 112 (rounded up from 111.11), which is a 12% increase in total firm value headquartered in my economy to make up for a 10% tax reduction. That's a rather high rate of elasticity that you'd almost never see in real life.
There are obviously diminishing returns to this - a reduction from 25% to 24% tax hurts revenue less than 10% to 9%, because 1% from 25% is a smaller proportion than 1% from 10%. But in general, reducing corporation tax is an extraordinarily inefficient way to increase revenue, if it works at all. It's a nice talking point that has some credence because people who only studied a first year course of economics deal with perfectly competitive frictionless markets, which means firms don't have to worry about infrastructure or staff. In such a world, the country with the lowest tax rate would have *all* the companies. But we don't live in that world.
