SP.... you can keep your existing BT mailbox ... however it will only be what BT call "basic mail".
I know 'cause I've done just that!!
You won't be able to set up outlook etc to head off and grab the stuff from your BT mail box. You'll have to log in to read it.
You also won't be able to set up to auto-forward your messages to your new ISP mailbox ... some (tiscali) do allow that.
I think you have to keep some activity going on the mailbox but that's not difficult .. given that BT seem hopeless at blocking spam!!
I had my BT mail account from the time I used to have a dial up modem.
One bit of advice I'd offer for your proposed "get all from sky".
I've stayed clear from that after it was pointed out that getting your 'phone and broadband from the same supplier means that they can "unbundle" you onto their equipment at the exchange - if they have it at your exchange.
As I understood it that means if you later want to change either/both you forst have to pay a fee to get off your current suppliers kit and back onto the BT equipment.
I'm told that if your "unbundled" supplier gives you a MAC number the other networks won't want to accept it without you paying the fee upfront.