For me, as an advanced learner, Game of Thrones is great for learning English. Whether it’s great for learning British English, I can’t say. I’m not sure learning British English is a priority for most learners. I have never sought to learn any particular type of English. I expose myself to anything in English as long as it’s interesting and Game of Thrones is very entertaining.

I don't watch it because I am learning the American accent only 

I've read books in Serbian. On the other hand, I've been watching TV Show in addition and I've also watched "Stories behind the houses" in English. I usually use English subtitles when I watch TV Show. I have difficulties in understanding some words due to different accents used by different actors. At the same time, I also find this very interesting because I've been noticing that our ears can easily get used to different accents. More than anything else, I find this TV Show very useful for practicing my listening skills. For instance, I always have trouble in understanding Ser Davos whether I watch his interviews or I watch him in the show. Maybe I just didn't get a chance to hear Irish accent so often and I am glad that I had a chance to do that with one of my favorite characters. This TV Show has opened doors to vary of dialects. Besides, that brought me to the conclusion that they've done a great job in assigning different roles for different actors. It gives to the TV Show the impressiveness and richness that we do not see often in other TV Shows. 

While there are a few quite antiquated phrases and terms e.g. 'milk of the poppy' and 'southron', the language used is correct, reasonably formal and mostly up to date.  The English accents are a mix of southern and northern (Yorkshire and the Northeast - John Snow/Ser Davros). The actor who plays Tyrion is actually American and his RP British accent is faultless!  In summary, I would say it certainly won't hinder your learning and it's a fantastic show.  Enjoy!