Further experimentation has followed. I have a test site that I use and I have upgraded this to version 5.3
Then made a new page called news and copied the page content code from blog to this.
Then applied it in navigation and on settings page have made sure that blog url and blog url prefix both have news set.
Now we have the same pagination problem as the live site.
I have created several posts with a tag apple in them.
When I click the tag I get a page of results.
When I click next page - the same results show. ie not the next page of results as it should be.
So the problem is not related to just the one site. But I think it is related to the change of title maybe as I have another live site running 5.2 where the blog page name is just unchanged and pagination works on that one.