BT will throttle P2P when their service is busy. They don't specify a time, just when it is likely. But if it isn't affecting you now then presumably it won't if you upgrade.
O2 have the traffic management shown on this page
Have you looked at Plusnet Extra, perhaps with the Pro option. (IIRC the Pro option is monthly, so you can try it and stop it easily). See this page
for their traffic management.
A good thing about Plusnet is it is easy to get out, even with the 12-month contract it doesn't cost a lot. You don't have to pay off the twelve months. Check that side of it if you consider them seriously.
There's no need to have your phone rental and broadband with the same company, except for a few such as BT. Many people, including me, don't like that anyway. My phone is with BT but I'm on my fourth broadband ISP. BT line rental is getting a bit steep now though, I agree.
If you use the landline phone much, remember to watch out for things like caller display and 1571 that others often charge for. We often see Primus mentioned here for the landline, and I don't remember any complaints. Possibly the Post Office is OK as well.
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost
. Internet connection -
IDNet Home Starter Fibre. Live BQM
"Where talent is a dwarf, self-esteem is a giant."
- Jean-Antoine Petit-Senn.