I had a P5 with its RB700 arm and first upgraded the arm to the one that comes with the P8, the RB880. Huge difference (already had the TT_PSU). Subsequently I upgraded the table itself and actually like the look of it, although I must say the improvement in sound is not nearly as much as upgrading the arm itself. I assume you have the RB330 arm on the P6, so I would start with the arm if you don't want to take the full plunge to the P8.
Also, in my experience, Rega's cartridges are not nearly as good a value as their arms and tables. Try a different cartridge/phono stage combo, remembering to stay on the lighter side of cartridges. FWIW I have a van den Hul MC One special with a Sutherland Insight with LPS. I am very happy and the stylus on the cartridge lasts an especially long time.
Just remember to make sure the table is well isolated from vibrations. I put mine on top of a Townshend seismic platform which sits on a wall mounted shelf. My floor is suspended over a crawl space, and the sound improvement from putting the table on top of the platform/shelf combo was a dramatic improvement.