as far as I understand, zero. If the portal is on someone elses land then they as landowner get to decide who can enter it (or most likely, not)
You could sink a shaft from surface down to the adit but this would need permission from the mineral rights owner as it would involve 'trespass' on their rights.
as a small aside, things like household foundations dont' usually encroach on the MRO's rights, but deeper things like pilings for wind turbines do. The MRO can then demand recompense for the rendering of any mineral unworkable (yes, even boulder clay, shale and other useless overburden)
The MRO cannot prevent you accessing their underground if permission is granted by the landowner, but they have definitely been known in the past to lean heavily on landowners, who are seldom keen to engage in a whose-barrister-has-the-biggest-wig competition
I am not a lawyer but I know a bloke down the pub who says his brother is. mebbe.
MARK