Sell yourself hard. References from the pupil master you've just left are not the way to do it. You've been on your feet for some time. You should, therefore, know more about the Chambers you are applying to than you did about the sets you applied to for pupillage. You also know more people who can give you the low down.
Flattery has to be at least semi-believeable.
The poor sod you're writing to has enough on his plate without listening to you moan. Don't give them an opportunity to do it. Remember, it is a legitimate test of your ability to ask whether you have told the person you need to convince everything they need to know. Type the letter - your handwriting is dreadful. Make an effort.