Some years ago my X-Type was sideswiped all along the offside by an errant foreign driver who forgot the rules of engagement on UK roads. He was held fully liable so it was a no fault claim for me. My insurance company scheduled the repair with their 'preferred and accredited' bodyshop; preferred because they worked down to a price even though the other guy's insurers were paying! The car was collected from my house and delivered back on a flatbed, only for me to send it straight back. It had:
Paint fingerprints on the nearside front wing (only the offside was damaged).
Paint fingerprints on glass.
No paint on the bonnet slam panel.
Unfinished paint on the top of the inner offside wing.
Bodge repair on the driver's door panel.
Poor paint finish along the whole offside.
Lousy paint job on the offside wheels which should really have been chemically stripped and properly refinished, not blown over.
The flatbed driver told me he had been reluctant to bring it to me as he didn't like the quality of work, but he was overruled by 'the boss'.
An inspection was arranged with an independent assessor, and the bodyshop was told to quarantine the car until he arrived a few days later (because the insurance company would then review the bodyshop's accreditation). They re-did the work instead and although he still criticised the standard of re-work he said "it was adequate for the price" and my insurance company then stonewalled. I considered legal action, but it wasn't worth the hassle as I wasn't keeping the car much longer anyway.
The bodyshop is a 'conveyor belt' operation that puts through hundreds of cars every year, and they actually told me they hadn't been paid enough to do a proper job. The insurance company is one of the biggest in the UK; I have always had a good driving record but was happy to pay a higher premium for a comprehensive and 'quality' policy - that proved not to be so.
My advice is to go where you feel happy, not where you're guided. Do check for any offloaded liability if you choose the workshop though, as imho insurers use every loophole they can.