Is it really necessary to sound British or American? That’s the question that some people ask.
While some of us prefer to sound a certain way (i.e. use a particular accent), the truth is, it isn’t much of an issue so long as you enunciate words and follow intonation patterns that are natural to native speakers. The goal of learning English isn’t exactly to acquire any of the native accents but more on being a competent user of the language, able to express your thoughts clearly in various communicative situations.
After all, countries where English is spoken as a first language also vary greatly in their accents. Let’s take the case of Britain. In the UK alone, British accents take so many forms that one region may sound drastically different from another. Accents that are commonly used include RP (Received Pronunciation), Cockney, West Country, and Geordie. For example, for somebody from Bristol, the letter «r» is pronounced after vowels so «mother» would be pronounced as «mutherrr» whereas a Londoner would pronounce it as «muthah».
Overall, while acquiring native accents may be admirable to some, it isn’t the main goal in learning English. So long as you have a neutral accent and can express yourself well, you should be good to.