Since the new EU cosmetics testing ban, the products can't have undergone any new tests on animals since the ban. I think
this explanation here is good from PETA.
According to this website, what your email said means that they don't test products sold in the UK on animals, but they do allow animal tests to be carried out by countries that require it - such as selling their products in China which requires some animal testing by law.
Personally, now that the leaping bunny symbol is so widespread, I only buy things without it if I can't find a satisfactory alternative elsewhere (or in a couple of circumstances on a case-by-case basis, such as with Lush or very small companies), as long as the company does have a policy against animal testing and the product isn't tested on animals... There's only one product I can think of that I still use that doesn't have the leaping bunny symbol, which is a make up remover, and I've tried every vegan one with the leaping bunny symbol I can find and they all burn my skin.
So I think it's up to you, and what you think is right.
I do wonder how much better things with the leaping bunny symbol actually are, now that legally products tested on animals can't be sold in the EU. I wonder if it'll be more relevant what the company does outside the EU - I think products with the symbol can still be made by companies that sell products outside the EU that are tested on animals, right?