Working with an accent reduction specialist would probably help you achieve the results you are looking for. It is beneficial to look for someone who is a speech pathologist and/ or certified in accent reduction. This person would have advanced training in how certain sounds are made and how to modify your speech to make the same sounds.
I offer accent reduction training via Skype anywhere in the world, but as I am American, I teach a standard American accent rather than a British accent. However, I am certain that there are accent reduction specialists who teach a British accent.
To your best speech,
Lisa Scott