So do Brad Pitt and Queen Elizabeth. And so did Laurence Olivier and Walter Cronkite.
There is no person alive who does not have an accent. The way you speak a language, say English, is heavily influenced by your first language, if it is different from English. It is also influenced by where you come from, the level of education you have had, the social or economic class from which you spring, and even possibly the ethnic group to which you belong. We all have accents.
When people speak of a person having an accent, they mean, pejoratively, that the person has a non-standard way of speaking a language, whatever the standard is in their mind or that of their audience. Clearly the standard varies sharply. Sir Laurence, who made a great deal of money by bringing his histrionic talent to the other side of the Pacific, did not at all sound like his Queen, and the avuncular newscaster Cronkite, so beloved of Americans, read his daily bulletin in tones very different from Brad Pitt’s.
Yet ridicule is poured on the Tamil Indian who has come to work on a network system in Alabama on a H1B visa or the Salvadoreño who has crossed the border from Mexico questing for cleaning jobs in a New Jersey suburb. Even more ridiculous is the superior air with which a person, who has spent some time in Bristol or Boston, looks down on the average denizen of Manila or Mumbai.
When I sat down to eat, I had a momentary flash of annoyance that a person, whose work is to fashion a sandwich from the ingredients in front of her, should have so much trouble following a simple order. Then I realized that, in a country where live 5o million people for whom English is a second language and in a city where the foreign-born outnumber the native-born 7 to 1, it was I, the customer, who should learn to cope with the limited linguistic skill of a low-wage server.
It is well-know that in the US people are discriminated against, in recruitment or in assessment of their work, if they seem to speak with an unfamiliar accent. Routinely, new immigrants are treated unfairly the moment they open their mouth, even if their looks are misleading. Even in jobs where the spoken language is not important, a prejudice against the non-native person masquerades as a bias against the non-native accent.

Of course, we want to be understood when we speak. Our intonation of words must bear a reasonable semblance to the expected sound of the words. This has become easier thanks to the internet. You can click on any word in a dictionary and hear the right sound, and you can do so in any major language. But to strive for the correct pronunciation is a far cry from the inane attempt to ape the ‘correct’ accent.

I learned English in India, including some mispronunciations, but never made the slightest attempt to speak like my English colleagues. Later, I was equally loath to pick up the midwestern accent most current in the US. My effort was, as ever in every language, to learn it well, use it with elegance and precision. That effort has not ended. It never will. I admire EM Forster and EB White, but I try to write in my own way, battling to find my own idiom.
Getting some preferred accent I believe to be a fool’s errand, unless one works in a call center or aspires to an elevated social status. I have no desire to seem superior to anybody else. A large part of my work involved making presentations to groups, big and small, and I never experienced blank looks. Nobody complained that I was unintelligible; rather, some complimented me on my clarity. That to me was more important than being noted for an Oxbridge accent or taken for a Boston brahmin.