The fastest are always on the local network, e.g. at your ISP.
You'd think so but you'd be amazed how many ISP's screw up DNS.
There is no advantage to using Google's public DNS (8.8.8.8 or 8.8.4.4) but if you were to use Quad 9's (9.9.9.9) or CloudFlare (1.1.1.1) then they filter malware domains.
I just remembered another advantage which is why I'm not exclusively using BT's DNS resolvers, they don't properly support DNSSEC which is important for ensuring the validity/integrity of DNS. If you use Google's public DNS, Quad 9 or Cloudflare's DNS you will get DNSSEC validation assuming your client device is configured correctly (you can test with this helpful website: https://dnssec.vs.uni-due.de/).
Well that's quite interesting about DNSSEC with a "Jack and Jill" explanation available on the Internet. And yes BTs DNS addresses do not support it, which IMHO opinion they should. Earlier in this thread there was mention of a tool to use to find the fastest DNS servers which when used shows the BT router failing miserably. Google DNS was much better but even they were surpassed by 47 others of which 9.9.9.9 was one.
Personally I would prefer to use a DNS server located in the UK which supports DNSSEC but they appear to be few and far between. It is noted that to use another DNS server then this thread says what needs to be disabled within BT.. Please be aware that this swap out is in a friends house who believes that BT is the bees knees when it is obvious that it isn't.
Add into the mix of problems of private domain names having difficulty in getting their emails through to BT email accounts and I would only wish end users would select a different ISP.