BT are currently doing a £30 new line connection, providing you take out an 18-month line rental contract. They will do the connection free if you also take out BB with them, but I wouldn't recommend that due to their onerous DLM.
For BB, consider O2 or Be, depending on her usage & if she already has an O2 mobile. They also do phone plans but I think there is not much saving over BT.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU BB => 2010: Orange 16 Meg LLU BB