I have Avon tyres (CR6ZZ 185 70's) on my BJ8 and they are really fantastic, they don't last too well but for the mileage I do that's not a problem. They're a competion based road legal tyre, very stiff side walls (which I think suit a Healey) and an old fashioned looking tread.
I've got a Mk2 Jag that had Vredesteins on when I bought it about 3 years ago, they were quite old and it was like driving on marbles, great fun but not too secure so I changed them for Avons which have transformed the car. Never driven a Healey with Vredesteins.