The UK supermarket price war echoed to the latest shots fired on Tuesday morning as Asda ploughed its largest ever investment into grocery price cuts and Tesco and Sainsbury were rumoured to be in the midst of their own significant price investments.Walmart-owned Asda said it had invested £300m into cutting prices for the first quarter, claiming this is its 'biggest ever rollback' as part of a previously announced £1bn investment in price cuts, while it was rumoured that Sainsbury's had reduced 600 of its prices on Tuesday too, in the second phase of the FTSE 100 reailer's price-lowering strategy.Asda said it had already trimmed many prices on thousands of products on 1 January, with a full suite of cuts across 2,500 "household favourites" and "basket essentials" such as milk and eggs as well as big brands, some until the end of January or March and some ongoing."We're going further than ever before, rolling back those every day, can't-live-without items at a bigger percentage than we've ever been able to do previously," said chief merchandising officer for food, Barry Williams."With hundreds of products at 50p, and even more at 15% less than normal, we're aiming to make a big difference for families in their weekly shop."Independent City analyst Nick Bubb said Asda's move was coming as Tesco was rumoured to be in the midst of making its own cuts."Well, with Asda already upping the ante, it looks like Tesco is at last going to join in the supermarket price war on Thursday and come up with a way of no longer over-charging its customers for their branded groceries," he said, citing grovery blogger Steve Dresser."Clearly Tesco must feel the price gap to their main rivals is now intolerable and they have to react," added Bubb.Dresser reported that Tesco is to embark on a price campaign that will go live on Thursday to coincide with the strategic update from chief executive Dave Lewis, with all stores to see new price communication around branded prices.Sainsbury reports on Xmas trading on Wednesday, with Morrisons announcing its own trading statement on Tuesday 13 January.