Hi Mike
Hornbeam isn't a very durable wood. Being durable under water is very different from being durable when merely damp - for reasons mostly to do with the level of available oxygen.
Unfortunatley hornbeam doesn't take preservatives very well either - due its density and the nature of its porousity.
Where the posts of your structure go into the ground you might find these work very well for you;
http://www.postsaver.co.uk/
I use them and am very impressed and find them very worthwhile. I guess you could just use a blow torch for a few?