Welcome aboard. If you go to the intro section and say hello to 8 of your new friends, you can post pix and we can give you a better response.

But I'll clue in on one thing you said: Your chain snapped after a year, and since replacement you can't get it onto the smallest sprocket/largest gear without the chain falling off.

Was the new chain sized to the old one before installation, or was it run full length out of the box? If it wasn't sized properly - and it was much longer than the original - it could produce exactly what you're describing. So it might be something as simple as removing a few links to match the original chain length. Don't know if the bike shop considered this.

You also state that a pedal snapped off early on. There is the possibility that the pedal threads could be re-tapped to accept a new pedal instead of a crankset replacement. Surprised that wasn't done, as it's not that difficult, unless the defect created by the snapped pedal was too severe. That way, the original crank could be saved at minimal expense & bother. Since you're dealing with Halfords, they might not have considered this, preferring instead complete replacement.

Since the Bickerton is a folder, the question might fit better in the Folding Bikes forum, where specialists (not me!) might have a better handle on foibles particular to folders.