Just by way of an update:
I drilled through the wall from the outside near the overhead wire anchor, being careful not to drill through the bath! I fed a new cable through past the old box with the filter, down under the bathroom floorboards, along the landing and up into the study leaving plenty of cable free at both ends. Then cleared away the foliage outside.
On the day the engineer was due to arrive I turned up with a packet of chocolate biscuits as a bribe! He was quite amenable once the situation was explained, and agreed to use the new cable and fit a new NTE5 in the study - AND couple up the now rewired existing extensions in exchange for more biscuits! As I suggested the cable going outside is covered by a new external j-box.
Result - another 2Mbps download more. So much for "it's a long line and as good as it can get"!
By way of an apology his ISP has now offered a 12 month FTTC subscription for no extra cost, and his daughter has promised to cover the extra thereafter, from Australia! She wants to use a videolink so their family can communicate. Line testing estimates now indicate better than 40Mbps possible.
So I'm quite pleased it got resolved in a way that doesn't leave him with an unofficial bodged wiring system, and he can watch the sport he wanted.