Any BT package that has "totally unlimited" usage will not be throttled regardless of traffic or time of day. The Home Hub can be swapped out for any ADSL router but I don't know about the 'modulation mode' as I'm on VDSL.
BT aren't necessarily the cheapest, but they do throw in some nice extras. Free WiFi Hotspots, Antivirus and newly annouced BT Sport are all things to consider. The only thing that I can fault them on is customer service via telephone which isn't great though you can mostly get by using the BT Care forums.
Any BT package that has "totally unlimited" usage will not be throttled regardless of traffic or time of day.
that's the bit I was going to ask about - make the BT Sport offer very tempting indeed.
Now, if I wanted to switch my line rental and Fibre broadband from Sky to BT Infinity 1 would (a) be able to keep the same phone number and (b) still have to pay the £30 activation fee ?
BT will not waive the activation charge unless you opt for Infinity 2 but you should be able to keep your number regardless of package. From what you've said, you're already on Fibre with Sky correct? I have heard of some issues with FTTC to FTTC migration but I don't know much more beyond that.