Just a quick update regarding Visa Extension Letters from the British Embassy. The Embassy stamps but does not sign the letter it emails to you. After being told yesterday by Hua Hin Immigration office that they would not accept the Letter I went back again today with printed copies (2) of the email the Embassy sent accompanying the Letter. This worked and I got my extension (under consideration until April 20).
I advise any Brits to do the same, it might save you a wasted trip.
TLDR : Answer Summary
The British Embassy provides Visa Extension Letters that are stamped but not signed. A user advises bringing printed copies of the accompanying email when visiting Hua Hin Immigration, as this helped them successfully obtain an extension.