I'm looking at eucalyptus trees on Google Images and I do see trees that resemble the one I'm identifying -- I didn't know they can grow in England!

Are they the only non-conifer that stays green all winter? I see other green trees at the moment in the same area (I'm in Wanstead E11) although not all look like this tree.

I'm fascinated by trees that don't shed in autumn as it's such a lovely sight to still see green leaves in the dead of winter while all other trees are bare.