They probably will anyway. The market for Internet services is worldwide and customers choose between legislative regimes as well as between suppliers. This will not be possible if there is any built-in requirement to enforce decryption. We could end up with the worst of both worlds. Criminals and terrorists will be able to use strong encryption and legitimate users will be discouraged from doing business with UK suppliers.
Openness is a pre-requisite of trust.
The proposed licensing criteria for key generation seem to assume that service providers would issue keys to their customers. This is obviously necessary for building confidence. If the only way to deal with UK licensed providers is to use keys that they provide, then many customers, especially overseas, will not wish to do business. Some of these customers will be technically competent in computer security or cryptography, most will be completely ignorant of it. Some of them will reside in jurisdictions where their past experience encourages them to be very wary of all government or law enforcement agencies.