Woodpecker like bird caught on wildlife cam, can you help identify?

Hi there, hope the video loaded ok, spotted this bird on our wildlife cam at 4:44 on Saturday morning, it was on the temporary fencing around our chicken run, can't quite tell the colours but I can see clear contrast on tail end and can see the tail feathers are fairly long, looks and behaves like a woodpecker but I am not sure it is, we get Greater Spotted Woodpeckers but this is't one of those I don't think.

On a chicken group I'm on some people have said maybe Jay and someone has said maybe a nutcatcher but they are rare aren't they? Can anyone here help? We are located in Bedfordshire.