Profile issues will be a different problem and not related to low speed single-thread whilst still getting high multi-thread downloads.
I check my IP profile (by doing a BT speedtest) quite regularly and it's always 77.4Mbps (or 77.39Mbps, or whatever equates to an 80Mbps sync).
It's never shifted from that level.
Some ISPs (certainly on old ADSL products) also have their own profiling system (the IP profile advised after a BT speedtest is your IP profile on the BT Wholesale system). If records are not kept up to date, this ISP profile could end up being lower [than the BTW one] and limit the speed, but this will limit total speed and not just single-thread speeds.
We still don't know the real reason, or why single thread downloads are so slow for only a fraction of FTTC customers but with the limited amount of information it does look like a single-thread throttle.
Quite why Speedtest.net reports around 77Mbps down (and 17Mbps up), whilst the TBB tester reports as low as 6Mbps down and rarely gives upload results higher than 7Mbps, is a bit of a mystery.
The mystery deepens when I can run a TBB speedtest on my XP (2002 version, XP-Pro, SP3) laptop and get 50-60Mbps down & 16Mbps up, yet immediately switching back to my W7 desktop gives TBB download test results around 30Mbps (at best) and back to around 6-7Mbps upload.
I think we're seeing two things (which are necessarily related): -
1. Some quirky difference between Java for XP 32-bit and Java for W7 64-bit, which affects the TBB speedtester (no other differences, both machines have exactly the same AV software and both wired Ethernet into the same gigabit switch - if anything; the W7 desktop is the more powerful of the two machines - double the RAM and a 64-bit CPU, with a 64-bit OS).
2. Some odd BT single thread throttle (because low single thread downloads are not confined to TBB).
vDSL2 FTTC Infinity with BT
DL Sync 80Mbps
UL Sync 20Mbps