If the air-bricks are admitting air to the cellar beneath the floorboards, under no circumstances should you block the air-bricks. You'll end up with dry rot in the floorboards above.
You do need ventilation through an unheated space where wooden beams plasterboard and flooring material forms one or more of the bounding surfaces. The Builder's advice regarding a vapour barrier and insulation is very sound. However, you do not need "a gale" through this space but you need to have a few air changes an hour - if you put in the vapour barrier and insulation you need fewer air changes. Ignorance and the widespread lack of heating tends to lead to too much emphasis on ventilation and designing it in, making UK homes very heat-inefficient and draughty.
It's just reminded me of a cellar I worked on, where the vents had become partially blocked. I reduced the number to just two air vents, but made sure they provided a good cross-flow.
Karl made the point about air flow. You shouldn't even "feel" the air movement. If you can, then it's probably more than you need. Good ventilation is all about "air changes". Continuous gentle movement to carry moisture out of the building.