If they have a pavement licence that says so, yes.
Web search "pavement licence". First result:
Guidance: pavement licences (outdoor seating) gov.uk
A pavement licence is a licence granted by the local authority, or deemed to have been granted, which allows the licence-holder to place removable furniture over certain highways adjacent to the premises in relation to which the application was made, for certain purposes. ...
Cites among other laws, "pavement licences", sections 1 to 10 Business and Planning Act 2020.
Section 7(1):
A pavement licence authorises the restriction, by anything done by the licence-holder pursuant to the licence, of public access to the part of the relevant highway to which the licence relates.
Questions:
Does a pub have a right to control the pavement outside it even if they have permission to place tables and chairs on that section of the pavement?
Yes.
But does this give them control of the section of pavement as though it was their owned or tenanted property?
Well, they can put removable furniture on it. They can't install permanent fixtures.
Surely this cannot be right, and the pavement licensee does not gain a right to exclude others from the otherwise normal public access and usage of the land?
The point of the licence is to give the licensee the use of the area defined by the licence.
If so, where does the business’s control extend to? Does it extend all the way the whole width of the pavement to the curb and road?
It extends to the boundaries defined by the licence. My understanding is a proper licence won't permit them to completely obstruct the pavement. Meaning there should be a passage or gap so that pedestrians can walk from one side of the area to the other.