Melkor, your voice is fine. What is that accent? Accents are just accents to me, but some folks put snob value on having the right one.
Brits might need to understand that the average American can't attach any significance to Cockney vs Midlands or any of that. It's all pretty much "Brit." The equivalent over here is that some who have a real southern mushmouth accent have been trained to believe they have to leave it behind and move toward some kind of American equivalent of the old BBC standard plummy thing if they want a successful career, but even that is no longer necessarily a universally held truth. Bill Clinton and Jimmy Carter both held on to their Southern voices and it didn't hurt them. There are a few places over here where people need to adjust their speech because, for instance, nobody outside the PeeDee River Basin can understand a damn thing they're saying, but that's another thing entirely.
All a roundabout way of saying don't worry about accents when there are so many more important things to worry about like why people think we're sneering when we smile at them, etc. :-) If I have the time and energy I'll record something in my native South Jersey piney accent and then we'll have a laugh.