Can anyone help me with this BT phone line installation, please?

Uxb

It is most likely that each property owner along the road (frontager) owns the land of the road up to the centre of the road for the length of their frontage.
This is the default position for a private or unadopted way (not being a pubic highway) where the ownership is unknown.
That means that you need to get the permission of each owner between you and the 'end' to let them put new cables either under or over the ground on poles.

The comms companies seem much more legalistic and hesitant that the likes of gas and electric.
The latter's attitude is one of "in the ultimate case we could apply for a statutory notice for us to be given the power anyway to put in the equipment/pipes so we are just going to do it and save anyone the bother of getting written permission"
The like of BT have equal powers but tend to want everything in writing.

I live on such a road and have seen both extremes - permission needed from each resident to sign on the dotted line and at the other extreme a statutory notice order through the post by recorded delivery to each resident saying we are coming to put a pipe in and there is nowt you can do about it.

I've found it much easier to deal with the awkward squad yourself
If you explain that their obstructiveness is causing you to lack a phone line they might be more amenable than if they get official letters though the post from BT couched in legal terms about needing everlasting wayleave to be granted.