Two weeks after Sainsbury's joined its big four rivals in slashing the price of milk, it has raised the stakes by offering shoppers a 30p cross-­promotion on eggs.

Shoppers who buy a four-pint bottle of own-­label semi-skimmed milk can get 30p off their next purchase of Sainsbury's Woodland eggs via an ­on-pack voucher.

The promotion would enable Sainsbury's to avoid having to cut milk prices further, said experts, and would encourage spend in another category.

Cross-selling was "a smart way of engaging consumers on a value offering around their core shop," said Aidan Bocci, chief executive of Commercial Advantage. "These are absolute basics of why you go into a supermarket, so a large number of people will see the ­offer."

The move comes two weeks after Sainsbury's followed Asda and Tesco in reducing the price of four pints of own-label whole, skimmed and semi-skimmed milk from £1.53 to £1.25.

Morrisons reduced its prices the following day, with Waitrose ­following suit this week. The move is unusual for Waitrose, which had refused to engage in price-slashing tactics on staples such as milk and bananas to match its bigger ­competitors.