Online AI sources uniformly and firmly insist that, no, it will not be sent/served by the court, and that this is the Claimant's responsibility, and that until this duty is fulfilled by the Claimant, which they normally have a period of 4 months to do, the Defendant will not be informed of the existence of the claim.
A professional barrister remarks that the court system is all a bit dysfunctional and broken these days, and treats its users more paternalistically and like children, so it will by default serve the claim upon the Defendant unless the Claimant asks it not to.
However, even if the Claimant does ask the Court not to send/serve the claim upon the Defendant on the basis that the Claimant prefers to do it by themselves, in their own time (of course, within the normal 4 months limit given by CPR unless subject to any ordered extension), the Court may well go ahead and send the Claim to the Defendant anyway, disregarding the Claimant's request (unclear if this is ostensibly so regularly done out of attitude/policy, or out of disorganised broken-/inept- ness.
But, what is the legal/procedurally "correct" way that the County Court of England and Wales ought to handle this situation, and what reasons may its various hearing centres' staffs have for deviating from this, and how regularly or often would one expect them to do this, particularly in the London area if anyone answering is familiar with that region of the County Court, or has specific experience with it?