I don't really see a reason why it would have an impact on recognized standards within the UK. There are quite a few countries outside of the EU in Europe and they're doing fine with this.
The fact you'll have to switch to a non-UK NB is an inconvenience, but not that bad. Many companies actually use NBs outside of their home country for various reasons (cost, delivery time, etc.)
(The fact a non-EU member can't host a NB for CE is understandable, but kind of odd nonetheless, especially knowing that the CE mark is recognized in many countries outside of the EU. Just a remark here. Not meant to be polemic.)
In the short term, the really concerning point IMO will be for UK NBs themselves - there's bound to be some significant layoff there. From some figures I got (may not be 100% recent or accurate), the UK was the country with the most NBs within the EU!
Now it's up to you guys to make it go in the right direction.