Wow... I never heard of white lavender. I looked it up and I think that means it is most likely English Lavender (not surprising I guess since you are in the UK) maybe Lavandula angustifolia 'Alba.' This article https://everything-lavender.com/white-lavender.html
has info about some of the options of what your white lavender might be. The article says the white lavender varieties are not as cold hardy as other varieties of the same species. But I think So. Yorkshire has very mild winters, about equivalent to our zone 8. So your lavender should still be completely hardy for you.
So I'm still not sure what the point of digging up and replanting it would be? What are you trying to accomplish?
If you were thinking of digging and dividing, like you might with irises, that does not work with lavender, which usually arises all from one main trunk. Lavender is usually propagated by cuttings or layering.