my first thought - is it a type of honeysuckle?

Mine too, but then I thought not.. hope somebody does know.

I thought the smaller round leaves looked a bit like Snowberry that grows around my garden (obviously white berries) but found one online called Symphoricarpos orbiculatus (Coralberry).

Thanks to everyone. So it's a bit of a difficult one to identify then. It's just appeared out of nowhere in the middle of my clematis bush and has almost taken over it!

There are Loniceras which are shrubs rather than climbers and they have berries like that, and they are very invasive from seed too.

It is a honeysuckle, probably lonicera maximowiczii, from the look of the leaf. Shrub up to about 4ft ish, and quite vigorous to that height. Flowers May/June?