Yes, it is!

And you know because...it's a Webley, like every other handgun used in every British period mystery show...identical grip, identical model.

And it was kept in the top right drawer of his desk.

And as for realism: if it's not an intact bullet pried out of a wall or removed from a body, it's a shell casing (as in last night's episode of Foyle's War).

There's still nothing better to watch, though.

Watch Midsomer Murders. Weapon of choice to snipe your victims: The 28 inch hammerless double barrel shotgun. With a rare Webley appearance.
Veddy British!