"Bob's your uncle"

[Jonathon Green]

No-one else seems to have dealt with this one, so:

It is, indeed, a UK coinage, and means everything will be absolutely fine,
there'll be no worries; sometimes prefixed by _and_. According to A.J.
Langguth, in his biog. of _Saki_ (1981), the phr. came from f. the
apparently nepotistic choice by the then Tory leader Robert Cecil of his
nephew Arthur Balfour as Chief Secretary for Ireland in 1900, a decision
that was both surprising and unpopular.

Jonathon Green