You're not going to get very far bolting a turbo onto this engine and running it on pump fuel. The compression ratio is too high, even though it is direct injection. The 'success' some people are having is greatly down to them running E85 fuel, which I don't think anyone stocks in the UK anymore.
There are also potential issues with running this kind of fuel. Sure, they may have checked out the fuel pump and injector compatibility, but there are other seals/o-rings etc. in the system which have to be compatible or they will fail over time with high amounts of ethanol present.
You only have to look at Subaru's turbocharged version of the FA20. For 300ps, they drop the static CR down to 10.6:1, which is a much more reasonable place to be.
If I were doing my own turbo conversion, i'd probably go down to about 11:1, run half a bar of boost on a suitable turbo, and be happy with whatever the result is.