You can do what's called "shadowing". Basically, find the accent you like, and then listen to the same text over and over again. Hopefully, you have a transcript of what they've said or can hear well enough to create one. Then just practice shadowing that accent (maybe even try recording your voice at the same time) until there's no difference. There are also many teachers (such as myself) who specialise in accent reduction and modification. You could have someone help you specifically on those areas.
I will say a few things worth considering:
1. Do you have a good ear for music? Are you good at imitating accents in your own language? If so, you'll probably be good at mimicking English accents given enough time and ear training. However, if you can't adapt to different accents in your own language, then it will probably be hard for you to do so in a non-native language.
2. What type of British accent would you like? The UK has a lot of different accents separated mostly by region but sometimes also by class/education level. If I were you, I would find an YouTuber (for example) with an accent you like, and then learn and follow their videos to work on their accent.