There are a few things that can be looked for on Broom at this time of year (and it's much easier when there are no leaves in the way!). They range from the very common and easy to find, to the somewhat more difficult but if you know somewhere with a few bushes you should be able to find at least one species.
Agonopterix assimilella larvae seem to be everywhere I look. They spin a couple of twigs together as shown below (although the silk may not be quite as obvious as in this example).
It is important that you gently pull the twigs apart until you can see the larva and check that it looks like the photo below. This is because the dreaded Light Brown Apple Moth has been recorded on Broom and makes a similar spinning. No doubt there will be other polyphagous species that also do something similar.
The other three species are all miners. In all cases they mine the most recent years growth so the mines will be found relatively near the end of the twigs. The mines of Leucoptera spartifoliella and Trifurcula immundella are, in my opinion, inseparable. Some literature states that one species mines up the twig and then back down, whilst the other mines down the twig and then back up. However in my experience this is not reliable. My pictures of the mines are not great, nor are those I can find on the web but both mines are blackish as can be seen in the photo below.
The way to separate the species is that the egg of T. immundella stays fixed on the twig at the base of the mine, whilst that of L. spartifoliella falls off soon after the larva hatches. The photo shows the egg of immundella at the start of the mine.
If you want confirmation, you can carefully dissect the mine and look at the larvae which are very different:
The larva of T. immundella is shown above and that of L. spartifoliella below.
The final species, and perhaps the hardest to find, is Phyllonorycter scopariella. The mine is shorter than the two preceeding species and tends to be greyer or browner. The books say that the mine is 'inflated' and this is true if you use your imagination a bit!