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To my mind, it may be very difficult/nearly impossible to sound exactly like a native speaker, unless a huge amount of time and effort is made. For example, try to think of someone who is not a native speaker and lives in your country, but has been there for 5 years - perhaps you can still hear their accent and that may be the case somewhat even for people who have lived for a longer time.
Therefore, to my mind, I recommend trying to focus on moderating your current accent/style of speaking and making it sound more neutral where it differs from a British accent etc.. In addition, you can try to copy features of the target pronunciation that you are seeking to possess to make it more precise - for instance in Portuguese, they may add extra syllables such as "e-school" instead of "school", so try to minimise/remove this feature.
Remember, that in English it is not just the phonetic sounds, such as how you pronounce a word, but also the style of speaking. I have heard it said by non-native speakers of English, that sometimes they find it easier to understand those who are not native speakers. In that situation, perhaps the native speaker is linking their words together and also using more complex vocabulary.
For instance, a native speaker may say: "Ca n-I ha v-a cu p-of tea?", whilst a non-native speaker might say: "Can I have a cup of tea?" with minimal or even zero linking.