How to find accent tutors
To my opinion, the best places to find an accent tutor are the Actors Centre and the City Lit, both based around Central London. The Actors Centre applies exclusively to actors. The City Lit applies to individuals of every field, although there are accent classes for actors exclusively too. I've been there and from my experience as a professional trained actor is that in these two places a hard working actor who takes his craft seriously can find very good tutors. They have been teaching for ages the subject 'accent for actors' and know every detail of it. They show actors analytically step by step -both in theory and practically- what they need to do in order to 'improve'/ change their accent. They start from the scratch and can lead the actor to an advanced level.
They provide actors tapes and papers with the phonetics symbols and with words, phrases and full texts from theatre and various subjects in general. The students can also bring their own stuff with them too to work on so it's a good opportunity to have your audition piece with you; not only will you be shown the accent 'method' but will also be given the chance to work on the performance of the text too. Visit www.actorscentre.co.uk and www.citylit.co.uk.
But there is another thing you need to remember: accent work like any other work an actor is dealing with in order to evolve is something personal. There is hard work that is needed to be done from the actor's side. The tutor will show you the tools and the way of achieving something. To achieve your goal is up to you depending on which your goal is and how hard you are intending to work for it. So it's a matter of practice.