No, I've only see the 1 bill for my 2 lines and as I said in OP both lines are billed wrongly.
For completeness the bill for the non-1571 line reads:
BT Answer 1571
4 Jan - 15 Mar 14
This is the cost of your BT Answer 1571 up to 15 Mar 2014 at £1.75 a month ... £4.18
BT Answer 1571
4 Jan - 15 Mar 14
This is the cost of your BT Answer 1571 up to 15 Mar 2014 at £1.75 a month ... £4.18
BT Answer 1571
16 Mar - 15 Jun 14
This is the cost of your BT Answer 1571 charged in advance (£1.75 a month) ... £5.25
BT Answer 1571
16 Mar - 15 Jun 14
This is the cost of your BT Answer 1571 charged in advance (£1.75 a month) ... £5.25
BT Privacy with Caller Display free for 12 months ............................................... £0.00
30 Dec - 15 Mar 14
BT Privacy with Caller Display free for 12 months ............................................... £0.00
16 Mar - 15 Jun 14
I'd admit I'm extrapolating from my experience as I'm not anything special to BT.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC