I will second a vote for Alpher Instruments.
Not as well known as others, but they build exceptional instruments. I have been through most British built instruments and nothing surpasses Alpher for build quality and choice of woods in my opinion, there is no-one like them. They only build two different model basses and restrict a few options for customisation, simply because they believe the design they have is the best instrument they can make.
They give each instrument they build the proper time and dedication it needs. Some of the builders named in this thread churn basses out at an alarming rate, Alpher's output is much smaller (my bass was only the 30-something instrument they had built) and that is incredibly reassuring to me.
Me and Chris have become friends following my commission and the guy honestly couldn't be any better customer service wise. Immediate response to emails and Facebook chat messages before, during and most importantly after the build. They are a joy to work with.
Check them out, you won't regret it