A breakdown and an accident follow different rules, and mixing them up has real consequences. If the car stopped because of a mechanical failure, you can arrange assistance immediately, no report needed. If the car stopped because it hit something or something hit it, however minor, you need a police report before the insurance company will touch the claim, and in most cases a recovery vendor will not move an accident-damaged vehicle without one. Repair workshops are also required to see a report before starting accident repairs, so towing a dented car straight to a garage achieves nothing.
One scenario sits in between: single-car damage with no other party, a kerbed wheel that snapped a control arm, a pothole impact, hitting a road object. If you intend to claim on comprehensive insurance, you still need a report. If the damage is minor and you will pay for the repair yourself, you can usually treat it as a breakdown, but when in doubt, get the reference number; an insurer can reject a claim weeks later for a missing report you can no longer obtain.