I found one very likely Phyllonorycter tenerella (Joannis, 1915) Hornbeam Midget mine today - In this case much less than half the width of the available lamina between two side veins, and starting at the midrib running well over half the distance towards the margin. The mine was also inhabited, although having torn it open I may well have sealed the fate of this caterpillar to die before it achieved its further pupal and adult potential!
The picture below is of the mine from the upper-side of the leaf - well eaten and browned, narrow and tightly folded, and long. Interestingly there was some further feeding damage and even webbing at the ends of the mine - perhaps caused by something else, possibly a Tortricoid?
Phyllonorycter tenerella is a species of southeastern England, as well as of Europe. There are reasonable numbers of regular records from Kent, high in 2008 and 2009, as for other leaf-miners I think. David Solly seems to have been very good indeed at finding them over the years!
As far as other leaf miners go, there were also some (not many) Phyllonorycter esperella mines on the upperside of the leaves and quite a few Stigmella probably microtheriella mines running largely up and down the veins. I also saw a few galls caused by what I have called "vein mites" Aceria tenella (Nalepa).
The Hornbeams at Trosley are quite variable, some young, some older, some coppiced, some maidens. This one is a moderately young Hornbeam, apparently a maiden, never been coppiced. It does look possibly a bit root-bound!
This one is another potential maiden, but quite a lot older! This suggests that there hasn't been much coppicing going on in this are of this particular woodland for quite a long time. This might match the history of the wood as a private estate, rather than a worked woodland.
There is an older picture of the grounds on the internet, of unknown date, but indicating their amenity nature at that time.
I saw two trees that were covered in fruit, and wondered why the distribution of fruit was so unequal across the woodland. I collected a couple of dozen fruit to see if they could be germinated.