These are small (2 to 3 mm) but very distinctive weevils, black dark brown or blackish with antennae, tarsi and sometimes the extreme tip of the rostrum and tibial apices red. The larva mines the leaves of Beech.

Adult leaf mine

Adult: Unless identified by a recognised expert, photographic evidence is required and the specimen should be examined with a microscope. In the comments box, state the key or ID method used. Note the beetle's size and describe the identifying characters. It is advisable to retain the specimen in case further checks are needed.

Leafmine: Unless identified by a recognised expert, good photos are required that show the key ID features.

Typical habitat is broadleaved woodland with a varied shrub layer, wooded pasture, parkland and hedgerows where the host is present. They become active on evergreens during February and move to Hawthorn as soon as the buds burst, typically a month or so before those of beech. Adults feed on Hawthorn leaves as they open although this may not be the only host at this time. They will move to Beech as soon as the buds burst on that species.

Eggs are laid on young Beech leaves from April, as soon as the leaves open.  The larva mines the leaves, initially creating a narrow corridor leading towards the leaf edge from an oviposition scar in the midrib, which then widens into a large irregular blotch at the leaf margin. 

Peak time is May to September, but see above.

With the exception of Shetland this species is common and often abundant throughout the British Isles.

Fairly frequent in Leicestershire and Rutland.

http://www.leafmines.co.uk/html/Coleoptera/o.fagi.htm

https://bladmineerders.nl/parasites/animalia/arthropoda/insecta/coleoptera/polyphaga/cucujiformia/curculionoidea/curculionidae/curculioninae/rhamphinini/orchestes/orchestes-fagi/