Our valuation survey has come back £21k lower than our offer, £11k lower than original asking price.
(Therefore our offer was £10k over asking).
Appreciate we offered over asking but didn’t anticipate the survey coming in £11k less than the original asking price.
Would it be unreasonable to renegotiate our offer?
Not unreasonable at all, it's probably the most common approach after this happens.
It could have been a bad surveyor but in all likelihood another survey for another set of buyers would come back with the same or similar results so the sellers would struggle to get the offer they got from you to proceed unless someone was willing to fund the additional £21k in cash as the mortgage company won't consider it for their valuations.
Always worth a shot, even if you meet halfway and fund about £10k yourself and they drop £10k.