TM,
The Yak is a great advanced trainer - there's one available for commercial instruction at Skytrace, at Wolverhampton Spaceport. Another great advanced trainer, somewhat more widely available, is the Pitts S-2, which is about as different from a Tiger Moth as it is possible for another two-seat single-engine biplane to be. It's not far from Cambridge to Sywell where Northants School of Flying has one. Any owner of an under-utilised Spitfire would, I guess, look at someone with mastery of both Pitts and Yak as having at least an element of potential. And a Pitts hour and Yak hour together cost about the same as a single Harvard hour.
Air forces are very choosy about their pilot candidates (even in 1940) and don't mind washing out lots of them. In civilian flying everyone who can be trained to fly safely has the opportunity if they can find the cash and motivation, even if it takes longer with a steadier rate of progress.
But if you've only flown the Tiger don't overlook the benefits of broadening your experience with other types even if they appear less exotic. Learning in stages is a lot easier rather than lump it all together at once - less risk of "swamping". If you go straight from Moth to T-6, you would miss out on the experience of all the shades in between and may find it a lot more intimidating than it need be. You might also miss out on a lot of fun.
Having gone Warrior - Archer - Arrow - Yak in the nosewheel world, and Chipmunk - Super Cub - Pitts - Moth in the taildragger world, each transition has helped the next. I'm _very_ glad that I did some training on the Arrow becoming accustomed to CS prop and retractable gear in a familiar environment before I converted to the Yak. I'm also very glad that I refreshed my tailwheel experience with the Cub before trying the Pitts. And no, I am not yet its master, not by long chalk!