Hmmm
That's the message I'd expect if you were actually being directed to something that wasn't BBC.co.uk
A couple of things to try:
Try searching Google/bing/other for BBC and BBC sport or BBC news.
See if the links from a search engine work any better...
Also try pinging BBC.co.uk
Open a command prompt and type ping BBB.co.uk[\b]
Let us know the returned IP address
It's really unlikely, but if you are somehow getting redirected somewhere else, we should be able to tell from the IP address.
Assuming there's nothing nefarious going on, then it would suggest something is a bit funny with the certificate you're receiving from the BBC site.
I'm not sure if the exact location in Brave, but near the address bar somewhere, you should have an option to view the certificate.
It's normally where the padlock icon is shown.
(MS Edge has a link where it says "connection is secure" that will then allow the certificate to be shown)
If you can get to the certificate, you want to see who it was issued to, by, and the valid date range.
That info may provide some clues