My daughter is pretty small & we went through this struggle. I got her a Carrera Star at the start of lockdown from ebay, although that is a 14″ wheeled bike, rather than 12″.
We tried a couple of 12″ bikes in a local bike shop just before lockdown & she couldn’t pedal them – the geometry was really odd to fit everything in and she just couldn’t turn the pedals.
The Star is similar to the Carrera Cosmos, but with a dropped top tube.
She’s moved onto a Ridgeback Dimension 16″ now, so I’d be happy to let the Carrera go for £30.
We are near Peterborough if that’s any good to you?
I’m happy to measure any dimensions you need – lowest seat height etc.
Condition is generally good, although the grips are discoloured – I think the previous owner let them go mouldy & they never cleaned up completely. And the chain guard is cracked – someone dropped another bike on it when she was at nursery & broke it. It’s currently taped up. I keep meaning to go a better job on it, but never find the time.
Anyway – on the whole it’s sound. Decent Tektro brakes with small levers, Kenda tyres and a similar weight to her friend’s Frog bike – might even be a bit lighter.
Message me if interested.