I used to have Sky tv (a few years back) but now have Freesat and also Talktalk.
BT TV use a YouView set top box.
YouView set top boxes use a rooftop aerial for ordinary viewing and Internet connection for Catchup, On Demand, etc.
As part of my ISP package I have YouView Talktalk PVR box (signal via roof aerial and internet). I also have a FreeSat PVR box (free to view channels signal via Sat. dish) and can swap between the two (actually three as TV also has its own freeview built in)
A sky box continues to get Freesat free to view channels when/if you end your sky subscription.
Only time I get any problems is in bad weather which sometimes affects rooftop aerial signal. Ditto for the Sat dish. Not had any problems viewing content via Internet (FTTC)