Is there any simple way to filter out the colour carrier on a video signal to reduce the spotty patterned look of a colour programme shown on a monochrome set? I thought perhaps a tuned circuit could be wired into a video lead to reject the colour frequency. Worth trying?

Well worth trying and nice thinking because you've basically thought of the answer yourself.

You'll need to fit a narrow band notch filter tuned to 4.43 MHz (colour subcarrier frequency) in between your video source and RF modulator. Designs vary and I've never tried one myself so I can't offer much practical advice as to where to get one or how to design one.

The few circuits I've seen are fairly simple LC circuits so building one should not be too hard. Impedence matching of the video input and output would need to be considered as well to preserve signal quality.

Ideally you want to avoid having to filter out the subcarrier to get monochrome video as you will loose some picture quality.
Depending on your video source you may have access to a monochrome composite video source already. Most modern set top boxes etc have component video out. The one marked Y (green colour) is a luminance video signal with no colour information in it. In other words it is pure monochrome composite video.
S-Video connectors also have a straight luminance signal as well, so this is another sorce of monochrome video if you don't have component video.

Andrew