Hawthorn has a common name of Mayblossom as it tends to flower in May. So not too late yet.
as for pruning it is really a matter of choice . what are you hoping it to do? be a hedge specimen bush/tree?

How old was it when you planted it?

I want it to grow into a tree - the only reason I think of cutting back the side shoots is that they are so long [about 4 ft] and whippy that I am afraid they will break in strong wind.
When we had very heavy rain all day and night one of these 'arms' was bent right over to the ground, I have since tied it to the fence, but what about the others?
I don't know how old it was when I planted it - got from the free 'plant a tree scheme' the year before last., so only a baby, it did nothing the first year and I thought it had died.

they are a naturally flexible plant anyway. does it have a main 'stem' that would become the trunk?
I would personally untie it from the fence and let it do its own thing. swaying about actually strengthens the main trunk.
when they first grew trees at the Eden project they had to introduce wind effects so the plants thickened up. Physio for trees made me smile :o)

Yes it does have a main stem and that is not tied up, something has been munching on it so gave it a quick squirt of 'Bug Clear' but I also sprayed a young Euonymus and it now looks very ill.

I should have known better because a couple of weeks ago Bug Clear killed all the flowers on my Berberis Darwinii - yet it says on it 'for flowering and ornamental plants'