I think it is important to understand the structure of an EV batteries when country of origin is being quoted.
EV batteries (more accurately called Battery packs) are constructed by taking battery cells and assembling them into small boxes called battery modules. A battery pack (which is a bigger box) is then made up by filling the big box with a large number of battery modules.
All of this helps to disguise the country of origin of the battery pack, as manufactures will claim to be assembling battery modules and battery packs (which they are) but the reality is that the vast majority of battery cells (80% globally) are still coming from China. Unless countries can competitively manufacture battery cells the rest of it is mostly packaging and some software thrown in to control the batteries.
If the UK / EU prevented the use of Chinese battery cells my guess is production of EV's would stop as there isn't sufficient battery cells being made in Europe.