A chain is not cheaper or better by default: every MOT follows the same DVSA manual and the same fee cap of £54.85 for a car. Compare with independent garages in your town with MOT near me.
Official sources consulted: DVSA active MOT test stations. MOT Test Centres is independent and not part of the DVSA or GOV.UK; fees and rules can change, so confirm on GOV.UK.