Update: the option to change your location has appeared again, so I can be more precise. Your location appears immediately above the date at the top left of the BBC homepage. Click on that and the option to specify your location appears.
There are times when it's not possible to change it (like now).
Usually the BBC home page has yor location at the top left of the page. Click on that and you can change it to your local location.
Update: the option to change your location has appeared again, so I can be more precise. Your location appears immediately above the date at the top left of the BBC homepage. Click on that and the option to specify your location appears.
Just seen your reply Puternut.
The option to set your locality seems more intermittent at weekends and when the option isn't there we all get London, even if you normally have it set to something else. When the option is there you'll see something above the date (postcode in my case). Try again tomorrow.
You can always click on "local news" and select your local area but it won't save it.