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...hazel leaves are soft to the touch - impossible to tell from a photo, of course! - whereas Elm leaves are rough to the touch.
Elm leaves are also often very lopsided (asymmetrical) where the leaf stalk joins the leaf.
And Elm leaves often have small warty bumps on them - which I think I can see in the first photo.
How to take close-ups with cheap phone and hand-lens:
Field Guides for Budding Botanists:
Lat/Lng: 51.595063888889, -0.12026388888889
OS grid ref: TQ303901