This author doesn't think much of the Global Britain strategy:
Britain’s defense budget and resources make it a “pocket-sized power,” unable to influence more than a handful of regions or fund these improvements. If the review becomes reality, Britain will become overstretched and redundant.
I don't see it that way.
It seems like the idea is to engage with many friends globally to bolster indigenous capabilities. With increments of direct military power available for escalation as needed--until American help is needed.
The overstretch objection would be real if Britain intended to commit decisive conventional military power across the globe. I don't think Britain thinks it can do that.
The strategy might not work. But the approach seems reasonable to me.