Some silver birch trees in the autumn in Sulham Wood
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Not quite sure what I'm picking out but the visible leaves look like hazel to me and the shiny trunks have the look of hazel or young oak which can both have a metallic sheen. Nothing jumps out as silver birch.
I am assuming that you are asking about the tree whose leaves we can see - and they are clearly Hazel, Corylus avellana.
The shiny trunks behind, as Steve says, do not look like any kind of birch.
Can you confirm if the leaves in your photo belong to the tree you wish to ID?
How to take close-ups with cheap phone and hand-lens:
Field Guides for Budding Botanists:
Lat/Lng: 51.4661, -1.0707
OS grid ref: SU646745