Hi Kate,
What the vendor and their estate agent are proposing is illegal. If you agree to it, you will pay proportionately less ITP (property transfer tax), which will make you complicit in tax fraud. If they won't proceed at the fully declared sale price, walk away. If the tax office decide that you have paid less for the property than the declared sale price, they can penalise you (not the vendor) with Complementary tax.
Kind regards,
Kim