Hi Matt, bit of a old thread but was looking for some other clubs I am near Warwick so not far from you.
Although expensive, there is also Honesberie Shooting club that I use every so often to zero Rifles and a bit of practice.
For small calibres there is Wedgnock Rifle Club in Warwick which is a lot cheaper but limited to below .22 unless its black powder I believe.
I haven't tried Jaguar Club yet, but thought about giving them a go soon. Have you been there yet? What's your take?