The british constitution is not non existant. That is a myth. It is different, being enshrined in the common law.
There are pro's and cons to doing it the British way and to doing it the French way.
Having it all spelt out in a single document doesn't make it free from abuse.
The british constitution evolves very slowly, and has done for hundreds of years. It is a fascinating thing to study and I actually think it is a superb foundation for Britains political and legal culture.