If you don't want to go to the hassle of reversing the polarity of the entire system, there are converters available to run a Negative Ground accesory from a Positive Ground system. Any decent auto radio shop should have a line on where to find one. One of the Sprites that I have in California came equipped with one when I bought it, and it worked just fine. But, a radio in a Sprite just isn't me, so now it's on a shelf out there.
I've never done a Big Healey, but have done Spridgets, and the odd Triumph, and it really was no big deal at all. On the cars with an electric tach, it entailed changing the impulse loop inside the tach, and not much else. Just remember to polarize the generator! One benefit of Neg. Ground (yes, I know I should say Neg. Earth)is that if you want to, you can replace the generator with an alternator.
Bugeye58