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I'm trying to get a look where there is basically a solid colour background, but with an invisible groundplane to cast shadows on.

Any bright ideas on how I could achieve that?

If I hide a groundplane then the shadows disappear.

I tried making like a curved backdrop type thing but it ends up being a gradient rather than solid.

I tried a custom alpha and then add the solid background in photoshop but lose the shadow I want that way too.

I think that what you want to do is to create your plane, apply a material which has both Shadow & Matte enabled (in the top-level material properties), and then make sure to enable Output > Channels > Shadow. Otherwise, please ask the question out in the main forum, since I'm far from being an authority on how the compositing features are generally used.