Titanium, Road and Flat-bar...is there such a thing?

[Jenkins]

You don't have to build it yourself - if you can get all the bits together there's plenty of bike shops that offer assembly. Pedal Power Cycles in Ipswich put this flat bar together for me based on a Pickenflick frame & forks and self sourced parts for £150

 

[jowwy]

But a titanium frame and build it to your own spec......

 

[Vantage]

As previously mentioned, Spa Cycles do their own range of hand-built bikes.
Usually the wheels are hand-built too and Spa will happily make any alterations to the bike that you request.
The closest thing I've found that fits your requirements is this. All you need do is ask for a flat bar, stem, brake levers and shifters of your choice that they have in stock.