to a degree.
There'd be a reasonableness test applied, so for example, if they'd hired an MCS certified company, which included scaffolding in the quote, and they went out to work leaving the company the key and instructions to get on with the work as agreed, then the householder would almost certainly have no liability at all in that situation if the company then didn't use any scaffolding.
If the customer was in, saw there was no scaffolding and raised it with the firm but was reassured they were using harnesses etc instead, but they weren't, then the customer's liability would probably be pretty minimal.
This would change significantly if the customer were the one that insisted the firm didn't quote for scaffolding, as they'd supply it, and on the day they didn't supply the scaffolding, or supplied unsafe scaf etc in which case there would probably be fairly joint liability.
How much liability was apportioned to the customer also would depend on how knowledgable they could reasonably be expected to be on H&S law - so an H&S consultant would be at least as liable, as probably would someone in the building trade, but someone who'd got zero professional knowledge of the building trade or H&S would be proportionately less liable / not at all.
TBH most customers could probably reasonably claim they'd done all they could by employing an MCS certified company, as MCS certification is supposed to mean the company has been checked, has health and safety policies in place etc. and should therefore be held liable for any breaches of those policies.
IMO - note I am not a lawyer.