Having just been through the CPLA to PPLH thing myself, and now going to work on getting comfy with flying both, I agree with the pile of terrific advice given on this thread.
My own extra- after completing the license I decided on a bit more training to cover techniques that are not in the Aussie PPL syllabus.
If the British situation is similar I'd recommend allowing about 40 hours for the license conversion training and test, then say 5 or 10 more for a bit of low-level, pedal turns, quick stops and torque turns.
These are items from the CPL syllabus that will sharpen your flying, and give you some options in your toolkit you will appreciate. Quick stops in particular might save the day in some situations.
Also I'm finding that autorotation proficiency slips, so need to practice autos with an instructor from time to time. See this as essential.