It's got nothing to do with 'trickle down' raging. It's simply that lower taxes encourage more businesses to choose to be based and taxed within the UK, which encourages them to employ and invest in the UK and to use UK businesses for support services such as legal and accounting.
Increased economic activity benefits everyone.
gf is correct that large numbers of companies have chosen to be based and taxed in Ireland, which has very low CT rates. In the late noughties, some British companies rebased there. This link is from 2008:.
https://www.nytimes.com/2008/09/05/b...ess/05tax.html
In 2009 the UK government changed the taxation of profits earned overseas and from 2010 onwards UK CT rates were lowered. The effect of that has seen some businesses returning to the UK from Ireland and a number of American companies choosing to operate from, employ people in and pay tax in the UK.
The trick is setting a tax rate that optimises growth and tax revenues - encouraging the golden goose to lay more eggs as opposed to slaughtering it for short term gain.
gf is wrong to say that the EU has stopped the Irish government from setting low taxes. The Irish are in bother for allegedly treating the taxation of Apple in a different way to other companies.
You talk a lot about the last 40 years. May I ask how old you are and what you remember of the time before that?