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They are free to do whatever they want. I see no basis whatsoever to ask for a discount if the surveyor has just been busy and not quite turned it around in the timeframe normally provided.
Im sure an apology and a thorough survey together with answering any follow up questions will be fine.
I absolutely hate the sharp elbowed culture of chipping people at the drop of a hat and for the most spurious of reasons.
Discounts are not litigations, just conversations about value and quality of service. We might disagree due to past experiences (it seems you have had difficult encounters with surveyors and discounts in the property world before) and that’s fine. OP is free to take any, some or none of the advice.