Hawthorns are very tough so I wouldn't trim them unless you think they need it for shaping the tree. No hawthorns round here are anywhere near blooming yet but I'd think it unlikely that a two year old would flower. Patience!

Thanks for that Snoopdog and Steragram.

I am confused now - there are lots of trees round here in full bloom for over 2 weeks, I had assumed they were Hawthorns [they smell nice, some are white blossom and some are a dark pink] they are not cherry blossom type.
What can they be if not hawthorn?
I note that you both live far away from the south east so maybe they just [usually - but not in my case] bloom earlier down here.

The trees you're seeing round and about could be Malus - Hawthorn usually flowers in May. Some varieties of Hawthorn are reluctant to flower when young, so depending on the variety you've got, the lack of flower may be to do with the tree's maturity.