Hi, welcome to the kitz forum.
This question would probably be best in the "Telephone Wiring + Equipment" section, however, no harm done and I'am sure one of the moderators will spot and move.
There are quite a number of ex BT engineers on the forum and at least one current engineer who are very well qualified to address your question, in the mean time and in lieu of their responses:
To the letter of the law the telephone/BB line up to the master socket should not be disconnected/re-wired, it's the responsibility of OR via your ISP, not sure what any charge implications would be considering that the current drop wire to internal wiring J/B has in fact fallen apart as you have stated.
My understanding:
The line has approx. 50v. DC across the pair. cores designated A & B, supply source, battery bank at the exchange.
Measured with respect to domestic earth, one line is approx. 0v., other line approx. -50v. DC, ie., the +ve line battery source is earthed at the exchange.
I can't remember which line is designated A or B, I'am sure someone will advise.
To answer your question regarding polarity, no, I don't believe it matters with modern telephone/BB equipment, either polarity should work.
However, please bear in mind the other points mentioned before proceeding with a more permanent repair.
Noted, reply by "licquorice" who is much more knowledgable on these matters while compiling.
Edit: Typo correction.