If it worked for you, that could be because when you changed your DNS server you also changed your public IP, or possibly because you used a service that doesn't just provide DNS but also caches content meaning you were accessing it without touching the BBC's servers.
There just isn't any aspect of BBC's geo blocking that cares what DNS servers you use, and if you go spend 5 minutes on Google looking into how geo-blocking works you won't find anyone talking about DNS servers being relevant.
I can't speak to your personal experience as I wasn't there, but I do have experience on the side of actually doing geo-blocking so I can say with confidence how that works. Apart from anything, the website / streaming service literally doesn't have any way of knowing what country your DNS server is in... the DNS server is just the thing that your computer asks "where does bbc.co.uk point to?" and it replies with the IP address for that domain. From the BBC's point of view your visit looks identical regardless of which DNS server gave that answer. There are ways of doing geo-blocking that are more complicated than just IP address (though BBC doesn't use them, it just goes on IP address), but none of them involve DNS.
I just did that search, and several pages talk about "smart DNS services" which also proxy your IP... not a single result suggesting that DNS itself is relevant.
The thing is, I'm not guessing, I'm someone who has actually spent time learning about how networking works, doing my first Cisco course when I was 17, and then in my adult career I've on multiple occasions been involved in implementing geo-blocking.
So I'm sorry if I haven't been clear, or have given the impression of being an idiot to the point that you think not worth listening to anything I say, but if you actually go and read up about how geo-blocking works you will find out that I'm not making things up when I say that BBC cannot tell the location of your DNS server, and if you've found that using a particular DNS service does bypass the restrictions then it still has nothing to do with DNS other than that the DNS provider is also offering you a proxy service.
>-- a site not being able to tell the location of your dns server, which is true
>-- your dns server not affecting how sites adjudge your location, which is not
Neither of these statements are definitively true/false.
1. Sites can most certainly tell the IP (and thus the location) of your DNS server. There are many sites that demonstrate this, just search for "dns leak test". Whether sites actually use this is another question.
2. Sites can serve different IPs (servers) depending on the DNS server, or even the client (through the edns client subnet extension). Some CDNs use this strategy to route requests to the closest server. However, this fact is a red herring when it comes to assessing whether "just change your dns to a UK server" is a viable strategy for getting bbc iplayer to work, because its geoblock checks based on IP of the http request, not through DNS.
There's also the question of "smart dns proxies"[1], which make it seem like all you're doing is "change your dns server to a UK server", but there's far more that goes under the hood than just changing your DNS server, because it's actually proxying your traffic as well. Changing your dns server to a uk server that isn't a smart dns proxy wouldn't get you pass bbc's geoblocks.
There just isn't any aspect of BBC's geo blocking that cares what DNS servers you use, and if you go spend 5 minutes on Google looking into how geo-blocking works you won't find anyone talking about DNS servers being relevant.
I can't speak to your personal experience as I wasn't there, but I do have experience on the side of actually doing geo-blocking so I can say with confidence how that works. Apart from anything, the website / streaming service literally doesn't have any way of knowing what country your DNS server is in... the DNS server is just the thing that your computer asks "where does bbc.co.uk point to?" and it replies with the IP address for that domain. From the BBC's point of view your visit looks identical regardless of which DNS server gave that answer. There are ways of doing geo-blocking that are more complicated than just IP address (though BBC doesn't use them, it just goes on IP address), but none of them involve DNS.