While the freeholders could withhold permission, the problem is that as a statutory installer, and the easements in the lease, they can pretty much go and do as they like in terms of installation.
However as the meter is on the ground floor the pipework to the flat is yours so that does not apply, and you are faced with routing it through as far as is possible existing conduits.
it might be that the cost and disruption to your neighbours is so great that they reluctantly accept that you are in law and under your lease entitled to a gas supply, and the threat of applying to the county court for their unreasonably withholding consent, that they accept the external pipework, routed as sympathetically as possible.
Based on the information posted, I offer my thoughts.Any action you then take is your liability. While commending individual effort, there is no substitute for a thorough review of documents and facts by paid for professional advisers.