Interesting to think about leafmines at this time of year.
I found some nice blotch mines on the upper surface of Hornbeam leaves at Dene Park this afternoon, which I thought must be mines of a Phyllonorycter species from their "general look". The most likely species should be Phyllonorycter esperella, (Goeze 1783), according to the pictures on the leafminer website. The species has an old synonym, Phyllonorycter quinnata, (Geoffrey, 1785).
Phyllonorycter esperella mines are generally found first in June, then again in September-October, specifically on Hornbeam, Carpinus betulus (L.). The young mines are roundish, on the upperside (generally unusual for a leaf-mine), usually centred over a side vein, silvery with brown speckles, and they then expand to be larger ovals, often substantially contracting the leaf beneath them as they do so. All these characters seem to fit very well the mines that I found today!
The adults emerge, like many other Phyllonorycters, first in May and then again in August as a second brood.
I don't think it could be Phyllonorycter tenerella, as although this species is found on Hornbeam, it is described as being on the underside of the leaf, from the midrib to the edge of the leaf, and quite narrow, generally between only two veins.
http://calderdalemoths.blogspot.co.uk/2008/09/phyllonorycter-tenerella-challange.html
Equally it is very unlikely (but not absolutely impossible) that it should be Phyllonorycter ulmifoliella, which normally feeds on the underside of Birch leaves. There is however one recorded instance of this species feeding on the upperside of Hornbeam leaves, noted in the Entomologists Record of early 2013 following the emergence of an adult from a mine collected in the autumn of 201.?
I also do not think it will be Phyllonorycter messaniella, as that is generally found on Oak, Beech or Sweet Chestnut, and less commonly on Hornbeam. On Beech and Hornbeam this species is found on the lower surface between two adjacent veins, with a sharp fold, so again this does not really fit the majority of mines found. However there was one mine, clearly different, and I thought it was most likely to be this! It started well out from the midrib, and finished well before the leaf margin, and fitted the pictures really quite well.