Exactly what happened to me 2 months ago. Morrisons car park, returned to car and had the same damage as you, but to my rear door. Saw the Manager, he reviewed the CCTV and told me he could see the incident, and, as the car drove from the car park they could capture the reg.No. Supermarkets wont release CCTV footage as it's against the Law (Data Protection) He advised me to report the incident to the Police, they will go to the Supermarket, check the CCTV and decide which way to progress. Waited 2 weeks, phoned police and asked for an update. "These cases can take up to 6 months to resolve, Sir''
Thought I may as well take this one on the chin. Had the repair at Lexus, £1050. Where the marks are on your door there is apparently a strengthening bar which makes the job that much more difficult, obviously.
A week later, a letter arrived from the Police stating that they had reviewed the CCTV and had been in touch with the other driver to remind them of their responsibility to other road users and supplied me with their Name and Insurance details but they will not be taking any further action. Received a phone call from their insurance 'Direct Line' saying they accept full responsibility for their driver. Told them I had had the repair done already, no problem Sir, send us the invoice. A phone call from them 2 days later, shall we make the cheque payable to you or the Repairers. Me, please, cheque arrived 2 days later, case closed.
Go back to Sainsburys, ask them to review the CCTV. If they can see the incident, then report to the Police. Hard to judge from photo but I would think that needs to be done professionally. I see your in Hampshire, if you're not too far from the A3, PM me and I maybe able to help you out. Best of luck, Graham.