See my answer here - https://news.ycombinator.com/item?id=9300690 - about why you're getting O2 for a Giffgaff number (Giffgaff is an O2 MVNO, and owned by O2's parent Telefonica as it happens).
Re: a Twilio UK landline number coming up as JT, as you're probably looking at the results of a SS7-MAP command that returns the SMS routing info for a particular number, in this case it's likely that JT look after the SMS side of that number (routing for voice and SMS and the networks themselves are generally quite separate).
For example the Giffgaff network is carried by O2, and a UK landline rented through Twilio appears to be carried by Jersey Telecom.