Yes you can quite easily switch from Sky to BT and keep your phone number. You do all that during the sign up process.
Although why do you want to switch? I find BT's customer service leaves a lot to be desired. Personally I find Sky's team a lot more helpful... Reliable network too.
I wanted to switch as it would be considerably cheaper and faster than upgrading to fibre with Sky.
I just used BT web chat, then they called me to answer my question but I'll be honest the customer service I received was some of the worst I've ever experienced.
The web chat was like talking to a 5 year old, they then said they'd need to get someone in customer services to call me.
He was happy to take my order over the phone and guarantee that I could keep my number but when I said I'd like to place the order online he got really short and said your on your own then.
It's really put me off going to BT, I think I'll just stick with what I'm on now.