I'm in the UK too, and find the plant-based phrase generally useful. For example, some double cream said 'plant-based' alternative and also had the Vegan logo.

I've never really thought about it, but I assumed 'plant-based' was for products like cream that would have dairy and non-dairy alternative.

Saying 'vegan' might imply it's only for vegans where plant based just means 'non-dairy' and might be billed as more inclusive.

I'm not too concerned about it also possibly including eggs, as I always check for vegan icon or read ingredients.