* Woolworths expects to pay up to A$300 mln to underpaid staff
* Law firm puts amount at A$620 mln; files class action
* Govt agency, the Fair Work Ombudsman, investigating underpayments
(Recasts, adds confirmation of class action being filed and investigation by government agency)
Dec 2 (Reuters) - A law firm has filed a class action against Woolworths Group WOW.AX for underpaying thousands of supermarket workers, saying Australia's biggest grocery chain should pay more than double its estimate for the shortfall in wages.
Adero Law said it filed the class action on Friday for more than 7,000 current and former employees of Woolworths Supermarkets over the scandal, which has drawn criticism from opposition politicians and prompted an investigation by a government agency. October, Woolworths said it had underpaid thousands of supermarket workers for years and would need to repay as much as A$300 million, becoming the highest-profile company to be caught up in wage scandals across corporate Australia.
Adero Law said it "considers that the underpayments disclosed by Woolworths to date substantially understate the wages owed," and put the number much higher at A$620 million.
Woolworths intends to defend itself in the proceedings, and said it hopes to make interim payments to affected current and former staff before Christmas.
"Woolworths Group believes the class action proceedings are without merit," the company said in a statement.
Woolworths shares touched a record high of A$40.04 earlier in the session, and were up 0.1% at A$39.805 by 0407 GMT.
Other cases of staff underpayments in recent years have included retail conglomerate Wesfarmers WES.AX , Super Retail Group SUL.AX , and jeweller Michael Hill International Ltd MHJ.AX among others.
Last week, Woolworth's Chief Executive Officer Brad Banducci said he would forgo his bonus following the scandal, while Chairman Gordon Cairns would take a 20% cut to his board fee. agency the Fair Work Ombudsman is investigating the underpayments by Woolworths. ($1 = 1.4736 Australian dollars)