Why Britain had no direct equivalent to SMS Wolf

Did Britain field a ship comparable to the German raider SMS Wolf?

Not directly. Q-ships were the nearest comparison, but Britain did not need an improvised breakout raider because its regular naval forces could operate at sea.

Wolf was a response to Germany's difficulty in sending conventional forces into the oceans. A disguised long-range raider could break out and attack commerce where a regular German warship could not operate freely. British Q-ships shared concealment but served a different purpose, drawing submarines into gun range rather than conducting the same kind of distant raiding cruise. Britain could deploy ordinary warships across its sea routes, so it had little strategic need for a direct Wolf equivalent.