"We assume intelligent design is false, a higher power cannot exist? Why not? Couldn’t a higher intelligence have sculpted the “big bang”, evolution, etc. etc. well...yes."
In science, and in math, you always seek the simplest solution. It's an issue of methodology. Any phenomenon should make as few assumptions as possible, eliminating, or "shaving off," those that make no difference in the observable predictions of the explanatory hypothesis or theory.
That's the reason for not engaging in speculations about transcendent 'higher powers.' In science it only leads to discussions and arguments that make no difference in observable predictions regarding natural physical phenomena. The only difference that injecting creationism into scientific discussions can have is to obfuscate and prevent science from proceeding, as the current U.S. administration has done.
If you want to talk about God, you should do so where it makes a difference; for example, in discussions about ethics and moral principles. Brits should be well aware of the tragic history of having government impose moral law.