OpenReach (which owns the copper cables and associated infrastructure) is BT-owned but has to operate totally separate accounts to BT. That's to ensure fairness, as BT then has to pay OpenReach the same price to access their services as other operators do.
So if OpenReach put their prices up, everyone else is likely to follow suit (unless they're prepared to reduce their own profits).
Post Office line rental at £15 per month (or the equivalent of just £12 per month if you pay for a year in advance) is still cheaper than BT's own basic line rental fee of £16.99 per month.
A relevant link:
http://www.bbc.co.uk/news/magazine-30273667