Used Bikes

My advice is to stay away from bike shops as 100 wouldnt get you very far with them, facebook marketplace is your friend. Look for shimano groupsets, stay away from amazon sellers and any bike with suspension as at 100 pounds that would be just excess weight with no real benefit. Feel free to message me particular findings for my opinion if interested.

Should be able to get something decent for between £100-200 off facebook marketplace as the last poster said. Check the frame for any signs of corrosion. Make sure the wheels are true and there is no movement laterally/vertically in the wheel hubs. Also check the cassette/chainset(cogs) teeth as well, good video on that here

Make sure all the mechanicals run smoothly. The gear changes work when you press the levers, the brakes don't stick or rub and nothing else is clipping or loose when you ride it. Some of that can be adjusted, but without prior knowledge it may be tricky differentiating between poorly adjusted and bent/damaged. Although a bit of squeal when the brakes are being applied is not a big deal

Make sure there aren't any cracks in the frame and other structural elements of the bike.

The fact that you're asking us rather than your daughter suggests you're just after something to ride alongside a child rather than a keen sports cyclist so in terms of bike style you want practicality rather than performance.

So make sure it's got all the bits that the racers/mountain bikers sometimes leave off for speed - mudguards, kickstand, bike rack - make sure it's a comfortable riding position rather than a forward leaning aerodynamic one. Internal gears inside the rear wheel hub are lower maintenance than a derailleur, but rarer.

Smoother tyres are ideal, the kobbly ones are for off-roading on loose surfaces like mud and are a bit more effort to ride on firmer surfaces. Tyres are fairly cheap to replace if you use it a lot though, so that's not a deal breaker.

bike shops are deffo worth looking at my local bike shops sell 2nd hand bikes below 100 quid

always ride the bike before purchase. you need to think of whether you are going to be cycling on road or off road.

for me it is the weight of the bike that is important. you want the lightest bike possible for the money. and when you ride the bike, test the gear changes are smooth as that is where old bikes can fail and the chain drops when you change gear.

We have a few community based projects in my area that are given old bikes and they then service them, clean them up and sell them on for minimal amounts. Worth having a look and see if there are any your way. Otherwise Facebook is your best bet.