The London Fire Brigade (LFB) was called to the scene at about 13:15 BST after the lorry trapped several parked cars on South Eden Park Road.
The LFB tweeted: "Going the 'extra mile' might have been the better option rather than trying to squeeze under a bridge in Beckenham."
Train services across the bridge were stopped as a result of the incident.
A spokesperson for Halfords said: "We would like to apologise for any delays and inconvenience caused to road and train travellers and will be working with the authorities to carry out a full investigation."
London Bridge trains on their way to Hayes were terminating at Elmers End before the lorry was cleared at about 18:30.
A Halfords lorry bearing the "We Fit" logo has got stuck under a railway bridge in Beckenham.