My partner has a second hand Pendeleton Somerby. We bought it for a song about three years ago. It had a flat battery but we managed to get it running again and it has never looked back ever since. If you like the Dutch style bikes it might suit.
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On the negative side - the brakes are a bit fiddly to keep in tune, but probably no more than any V brakes on other bikes. When I rode it, I thought the gearing was a bit low. By the time it gets to 15 miles an hour, my legs are spinning in top gear, but if you just wanted to go to work on a fifteen minute ride - two or three miles, it would probably be OK. They don't cost a lot of money and you could ride along happily enough. Her bike has been ridden 25 miles on a charge and does that even now when the battery is at least four years old. That said - it hasn't done a lot of miles and we looked after the battery when it wasn't being used. Often they get left all winter, and won't take a charge in the spring when the sun comes out again. That does them no good at all.
Like any second hand e-bike, you really have to hope the battery has been looked after. If you get one with a dead battery, it ought to be cheap, because you will be looking at about £300 for a new one. We bought my partners bike for £350, assuming it would need one, but it just woke up and worked.
There are lots of new, moderately priced e-bikes for sale. I am sure that those which are cheap, will have various compromises in the eyes of e-biking enthusiasts, but your requirement is a cheap, reliable, short range transporter. Any hub motored bike would likely fulfil the requirements.
I am sure there will be lots of responses offering other ideas in a few hours.
It is almost exactly a year since I bought a REALLY cheap folding e-bike from Argos. It is certainly not the best e-bike in the world, but I have done over a thousand miles on it and it works like new. I really like it for its convenience for knocking about or going to the shops when I run out of something. Just jump on it and whizz off. For all its faults (in the eyes of the enthusiasts) it just delivers, time and time again.
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