Brokers are also obliged under regulations to provide the best quote for they're client so brokers will shop around for the best price on behalf of their client.
You must be joking. They will not shop around unless you threaten to leave them and go else where. All they do is give you the renewal from the current insurer.
As regards to automatic renewals I have noticed on my insurance certs that they are often issued months before my renewal dates. Seems standard enough practice with brokers.