Having no downtime is not actually achievable.
a) Phone. This will be re-jumpered in the exchange and then will start again. I assume you are looking to move sky talk back to BT and or some other telephone provider, based on the BT service. When I went from BT to sky the phone line was off for about 10-15mins, while the work was done.
b) Broadband. If is normal ADSL BB (not fibre) you get sent a modem. On the day of change, at some point the SKY broadband stops. You then need to plug in the plusnet modem and start BB again. I left for work and when I came home the BT based BB was off and the SKY one was installed. Again in reverse it should take the engineer 10-15mins to do the work.
c) for FTTC its the same as Broadband, but you may get an engineer visiting to change the BT socket on the wall. If so they will ring you. It took about 20mins to 1/2hr to go from ADSL to FTTC for me.
d) just starting for FTTC is self install. You get sent a new modem from the likes of plusnet and like Broadband, you plug that into the phone socket filter just like your existing modem. Again you wait until the service stops and then plug in.
So overall its around 1/2 hr switch over to about 1 hr. More than that you are unlucky and its a call to the new ISP support line.