Can a body shop increase their charges to match an insurance payout even if their original estimate in writing was less?

Question Details:

A lady hitmy car. Her insurance accepted responsibility, looked at my car, did the estimate and cut me a check for the amount of their estimate. I took the car to a bodyshop. They did an estimate in writing and it came in $400 less than the check that her insurer wrote me. The bodyshop asked me to bring in the insurance estimate when I dropped off car. When I wentto pay for the work, all of a sudden the total was now the exact amount of the insurance estimate, not the original estof the bodyshop itself. Is this legal? Can I refuse to pay anything other than the original estimate amount (which I have in writing)?

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