Which of the many "British English" accents are you seeking. To name a few: Geordie, Scouse, Yorkshire, Brummie, West Country, Cockney? There's an estimated 40 different accents in the United Kingdom.
There's also approximately 30 distinct accents in the United States. I'm Canadian. My personal diatribe . . . We all speak English! Not just "British or American English" . . . English!!!
I'd like to learn Chinese with a Chinese accent! Mandarin? Cantonese? Fujian? Odd, I guess that not all Chinese people speak with the same accents and dialects. Let's conclude that there are different accents and dialects in English-speaking countries as well.