I want to be armed with a few for arrival, and am wondering if I'm going to have to stop in an airport shop on the way to ME or if I'll be able to get some in the UK?
With the dollar being such a popular currency they will have plenty of each denomination and should be able to give you what you ask for.
If you are concerned that they won't be able to meet your needs then pop in the week before you need them and order some in advance.
Whenever i've got currency i've asked for some singles and been given $5-10 worth most of the time, if they're very low on them sometimes they can't but there are stores/eateries at the airport where you can break a larger bill if need be