Bike advice - wobbly back wheel

Hi all, I’ve just discovered the back wheel of my bike has an alarming amount of play in it. The bolts joining it to the frame are tight so it’s wobbling on its axle. I’m wondering is that something that sounds fixable and if so is there anyone kind who could help me fix it some time? Thank you!

I would initially guess the wheel is out of true likely due to a broken or loose spoke. Have you checked to see if all the spokes are ok? (squeeze each pair together to check they’re all roughly evenly tensioned)

Your cone nuts need tightening: https://www.sheldonbrown.com/cone-adjustment.html

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does anyone know if there are cone spanners in the bike repair kit at the space?
If not I have some and am intending on coming to the space for most of thursday evening, so could bring and would be happy to take a look if that’s a good time? (Edd’s probably right I reckon)

Hi all, thank you! I did some googling and I think it is the cones and maybe the bearings need replacing too. I’m away now for a week but would love to bring it in one day/evening in the first week of June if anyone will be around then who knows what to do? Thanks!

Which wheel (front or Back) and what size is it?. sure i’ve got one in the garage if you need ?

Courty