Identification

Does anyone know what varieties these are please?

All I know is that one is a rose (Last I remember I saw a white flower on it which were few and far between)

And the other is a deciduous Honeysuckle which had small double white flowers in spring and now has little red berries

I cut the Rose right to the ground late last year and it came back as vigorous as ever! Although it has not flowered yet.

The second shrub looks like lonicera maackii http://www.bluebellnursery.com/catalogue/trees/Lonicera/L/1670

I think the rose is the rootstock that another rose has been grafted onto, and the grafted rose has died.   Did the bloom look something like this?  If I'm right then it'll grow into a big bushy plant but you won't get many blooms.  Far better to dig it up and pland something else I'm afraid 

Yes it was something like that. The suckers just appear randomly around the area. I will check to see what flowers appear this year then maybe I'll consider digging it out. It has been there for quite a long time.