Hydrangea macrophylla usually are not pruned at all, except to remove the old flower heads back to a bud. They flower on old wood, that is branches grown last year.
However if they are getting big then you can remove say a third of the oldest branches, about now, to encourage now growth in Summer.
The pictures are upside down so not easy to see. It could well be Hydrangea grandiflora Annabelle though.

The second picture looks like a Sedum to me, possibly S. spectabile or one of its relations.

I think the second one is a Sedum too..It's ok to cut all the stems off,as it's very hardy..I leave the flower heads on for the winter,as I like the colouring,.You should be able to see new growth at the base now..

Thank you very much for the replies, should I cut off the old dead heads now just above the new buds or just leave those too? The pictures are showing the right way up on my screen so am not sure why they are upside down to view your end.

Sorry owdboggy just realised you answered that first time round!! Thank you

Are the two pictures of the same plant? As one is white and the other brown/
Upside down images often happens when posted from various devices.

Hi Abigail..it's up to you when you cut off. The dead flower heads on your hydrangeas. Some people leave them until the new buds break, as they offer some protection from frost. The Sedum similar... When you are ready just cut the stems right down to ground level.

We're you asking about the shrub in the second picture? If so you probably need to wait for the leaves to break.

I get it n ow, the first image is the H. macrophylla and the second is the unknown.
Definitely Sedum, I cut ours down almost immediately after flowering or they seed everywhere.

Thanks so much for comments - very helpful, new to this and a lot to learn so fantastic to be able to access this help!