How to speak British English?

I think the best way to learn a particular accent is to expose yourself to an environment that makes you practice it in day-to-day life. So, going through Netflix, British radio, and podcasts are good ways to understand how others are doing it, but learning won't be as effective until you practice it regularly.
I suggest joining some speaking groups on social media or finding people with similar interests to practice and listening to podcasts or streaming services.

I suggest you start with the sounds - vowels and consonants.
Watch as many videos related to pronunciation. You even can practice using apps available on the internet. Apps such as Learn English Sounds Right, and Sound Pronunciation App can help you improve your communication. These apps can help you work on your English phonetics. You can easily compare your pronunciation with the one provided in the app.

India follows British English. So if you are speaking English in India without any MTI or accent, then you are technically speaking British English. Then comes the British accent for which can only be learnt through listening. So listen to many movies, videos on youtube, and the BBC news (this is how I started). Watch the film 'sound music, 'my fair lady' ' and many more British movies, songs and videos. But the only way is to listen and practice it: practice practice and more practice.

Some quick and practical tips that you can apply immediately-

1. Start with the Rs -don't pronounce the r, but draw out the vowel and maybe add an "Uh" (here is "Heeuh").
2. U's- pronounce 'u' in stupid and in duty with the 'ew' or "You" sound.
3. Heavy consonants- enunciate heavy consonant words. Pronounce that t in "Duty" as T: not as the 'd' as doody so that duty is pronounced dewty or a softer jooty. Pronounce the suffix -ing with a strong g. This way, it sounds like -ing rather than - een.
4. Sometimes drop the ts-so "Battle" might be pronounced ba-ill.
5. Listen to the "Music" of the language. All accents and dialects have their musicality. Pay attention to the tones and emphasis of British speakers.

I hope it helps!

I learnt to speak the British accent by:

1. Listening to BBC Radio; was the first task I did when I wanted to acquire the British accent. 
2. I watched a lot of British series, especially the classic ones. 
3. I downloaded few dictionaries of British Slangs 
4. An English dictionary with the British and American accent, and a tad knowledge of International Phonetics Alphabets.
5. I took a text from classic British literature, recorded it on the phone, listened to them and compared it with the actual British accent. 

The above mentioned are the simplest way to learn British accent and British way of communicating.