I'm grateful to have found this post because I am having the *exact* same issue as you it seems.
Ever since 'upgrading' (were already on fibre, but now on fibre plus?) in around October, I've been experiencing severe ping/latency problems. I'm usually playing games most nights and have noticed that not only do I randomly experience spikes, but if anybody else in the house opens a Youtube video, watches Netflix/Amazon, Twitch or even watches a WhatsApp video it causes huge spikes and sometimes a constant higher MS making gaming pretty unbearable.
I have contacted BT 4 times, registered a formal complaint and they have still been utterly useless and unwilling to help. Each time latency is brought up, they say "this is to do with gaming right?" and suddenly it's as though all interest is lost entirely and I feel as though the issue is being swept under the rug. They keep reiterating that the download and upload speeds are fine, and that is the only thing that is guaranteed; latency does not come into it at all and is nothing to do with their service. I have voiced my concern several times about how unacceptable this is, but I have still gotten nowhere.
I have however been told that I can pay an *additional* £10 monthly in order to speak to the tech team, which is frankly ridiculous when I am already paying ~£65 per month. For this price I would exceptional customer support when I ring up with an issue, not told that I need to pay extra just to even speak to someone with knowledge. I was also told by a manager on duty that an engineer callout would likely "not help" as they only check that everything is physically working.
I have been sent a new Smart Hub, which changed absolutely nothing. I have also tried forwarding ports as per suggestion of the manager, which again did not help in the slightest. Tests done over the phone suggest that everything is working as it should be, and that I have not been throttled in any way.
At this point I too feel as though switching ISPs is looking like the only option, as no one at BT seems interested in looking into this issue.
I hope someone is able to offer some advice.
Still looking for a response as I'm having absolutely no luck with the customer support over the phone.