Hi, I'm hoping to change my BB to that of an old style square tapered BB. The reason for this is that the chainset I've chosen is a square tapered style

I'm hoping this is a common and easy thing to do. My bike is a boardman comp aluminium frame with carbon forks.

I am looking to transform the whole bike into a vintage looking fixie. I'm content with the other parts. I'm just struggling to identify what length BB I will need.

any help greatly appreciated

Yes, you can install a square tapered BB. That's not a problem. It is a common and easy thing to do, as you say. However, converting a bike with vertical dropouts into a fixed gear is neither common nor easy. Sheldon Brown explains: https://www.sheldonbrown.com/fixed-conversion.html

After reading Sheldon's article, google "magic gear"

So is the bike a brokie now?

As far as the entire project get something that has track ends or at least semi-horizontal dropouts if you are stuck on going fixed. Yes you could magic gear it and get a White Industries Eccentric Hub but honestly get a bike designed for being a fixed gear. Also a modern bike won't really look like a vintage bike with tapered carbon forks and modern aluminum tubing.

In terms of B.B. length that will be determined by your crank. Check with the crank manufacturer to see what they suggest or if it is something vintage check VeloBase or Sheldon Brown.

Me personally if I had to go with a square taper crank it would be the Sugino Super 75 which uses an ISO B.B. in 109mm or the Phil Wood Track Crank which is JIS 103mm. However I am quite happy now with my Sugino 75 Direct Drive because the outboard bottom brackets are a bit easier to work with..

I don't know what length bottom bracket you'll need as that'll depend on the crankset and the chainstay. I do not that buying a Half-link can make a big difference in getting the proper chain length with the gear combination you choose.

Cheers