This is a small phrase with a large consequence, and it is the reason some basements and some heavily loaded extensions get redesigned late. The Act treats foundations containing an assemblage of beams or rods intended to distribute load as special, and gives the adjoining owner the power to refuse consent to them being placed on their land. That is a genuine veto rather than a matter for the surveyors to balance, and it is worth knowing about at design stage rather than at award stage.
What makes a foundation special
Reinforcement. An ordinary mass concrete or trench fill footing is not special; a foundation containing an assemblage of beams or rods designed to spread the load is. Piled foundations with reinforced ground beams, and reinforced rafts, are the usual candidates. The distinction is about what is in the concrete rather than about how deep it goes or how much it costs, which is why an engineer's drawing rather than a builder's opinion settles it.
Why the adjoining owner can refuse
The Act requires their written consent before special foundations are placed on their land, and it does not require them to be reasonable about it. A neighbour who refuses is not obstructing the process, they are exercising a right the statute gives them, and no surveyor can award it away. The practical effect is that a design relying on reinforced foundations crossing the boundary is a design that depends on somebody else's goodwill, and that dependency should be known before the drawings are finished.
What a designer does instead
Keeps the reinforcement on the building owner's own land. That usually means an eccentric or cantilevered foundation designed to work without projecting under the neighbour, which is more expensive and needs designing rather than adapting on site. Where special foundations are proposed, the party structure notice must include plans, sections and details of construction together with reasonable particulars of the loads they will carry, so the neighbour and their surveyor can see exactly what is being asked for.
Questions people ask about party wall special foundations
Is a piled foundation always special?
Where the piles are tied with reinforced ground beams, in practice yes. An engineer's section showing what is in the concrete is what settles it, not a rule of thumb.
What if the neighbour refuses after work has started?
That is the expensive version of this problem, and it is why the notice has to carry the plans and the load particulars up front. Consent is asked for before, not during.
Can the surveyors overrule a refusal?
No. Consent to special foundations on the adjoining owner's land is the owner's to give or withhold, and an award cannot substitute for it.