It depends on five factors:
1. Your age
The earlier you start speaking English the easier it will be for you to talk like a native English speaker. When you start speaking in your native language your tongue, lips and jaw muscles are trained for your native language and the older you are the more difficult it would be to retrain them for English.
2. Your environment
Even if you live in an English-speaking country but your family and friends, peers and teachers speak with foreign accents you will unconsciously copy their accents. If you listen to music, watch films and news in your native language and not in English that too will contribute to you having a foreign accent. If you want to speak like a native English avoid speaking in your native language.
3. Hearing abilities
If you have good hearing abilities your chances of speaking like a native are higher than for those with poor hearing abilities
4. Time and effort you are prepared to invest in mastering English
To learn to speak like a native train daily for 10–30, rather than once a week for two hours. Regularity and consistency are the key.
5. Method of learning English and teachers
Choose an effective method with professional apps and a qualified speech tutor.
We had many students with strong foreign accents who told us they had a degree in English. In EFL colleges pronunciation is often neglected and qualified speech/accent tutors are very rare. The difference between an English teacher (TEFL) and a speech or elocution tutor is vast. EFL teachers focus on grammar, use of English etc, whilst speech tutors know how sounds are formed in the mouth and by listening to students they know exactly if their tongue position is too low are the law position is too closed, for example.
In conclusion, I want to mention that there are many accents and dialects in Britain: Northern, Scottish, Cockney, RP and many others. RP or Received Pronunciation is taught to foreigners because it is understood around the world and is called Standard English. RP is also a compulsory accent to learn for actors in British drama schools. American accents vary too: Southern, New York, Boston, etc.. You can learn to speak with a General American accent which is an accent of educated American people who have mastered their speech such as news presenters, diplomats and presidents. It involves working on your articulation, pronunciation and intonation.
You can master to speak like a native with professional apps based on RP:
Elocution Lessons, Get Rid of your Accent UK1, and Fluent English Speech (British English) or American Accent App and Fluent American Speech (based on General American accent), and Power, Pitch, Pace, Pause.
There are also two accompanying video courses: Get Rid of your Accent Part 1 and Get rid of your Accent Part 2.
The apps are available on the AppStore and Google Play. The functionality is ideal: read, listen, record and compare your speech with the model (actors with perfect pronunciation were used to create soundtracks for these apps). The apps have spelling variations for all English sounds and mouth diagrams to help you make the correct speech organ positions in words, phrases and poetry.
When starting your practice with these apps, go to “How to use this app” and click on: the difficult sounds typical for your nationality, then click on your nationality to work effectively with a more focused approach.
The apps contain:
1. A CD function, recording and comparing functions
2. Spelling variations for all sounds
3. Fluency and difficult speech patterns exercises
4. Intonation and sentence stress exercises
5. Pronunciation and articulation exercises
6. Words, sentences, verses and tongue twisters to make your speech clear