> So why then does the bank of England have and need the right* to print as many USD as they need, whenever they want.
The BoE does not even "print" the GBP (except paper/coins through the mint), never mind the USD. Money in the UK, like most countries, is created by banks through credit issuance (loans, mortgages):
And if the US wants to cut swap lines, thus making people more nervous about using and holding USD, thus reducing USD as a considered safe haven… ¯\_(ツ)_/¯
I'm not aware of anywhere in the UK that can print US dollars legally. As far as I can tell, there's just two locations that can print legal US dollars - Washington, D.C. and Fort Worth, Texas.