It doesn’t work like that. The monarchy has a lot of power. Power comes from sources other than a formal entitlement to pass statutes or make executive decisions. There is power in fame and reputation and respect.
The Queen is very popular. If the wrong person insulted her badly enough and that person was prosecuted on some basis, half the country would cheer.
Not only can immigrants be elevated to the British nobility, but they can also be part of the nobility of wherever they’re from, in which case, in any situation where a British noble would be "my lord"ed, they would still be offered equivalent honors. Like, if a Japanese nobleman who’s considered equivalent to a duke is at the same fancy party as an English earl, the Japanese nobleman would be introduced first because a duke outranks an earl, never mind their nationality.