LONDON, July 16 (Reuters) - Britain's public finances are losing around £330 billion ($442 billion) a year due to weak economic growth, population ageing and ill health, according to estimates from a think tank that show the scale of the challenge facing the next prime minister.

The left-leaning Resolution Foundation said former Manchester mayor Andy Burnham, who is due to replace Keir Starmer in Downing Street on Monday, needs a new fiscal strategy to stop borrowing, public spending cuts and tax increases from becoming more painful.

About two thirds of the £330 billion hole comes from a slowdown in economic growth per person since 2007, it said.

In a report into what it called Britain's two-decade fiscal funk, the Resolution Foundation also said:

• the triple lock system for increasing the value of state pensions should be replaced with a less expensive link to average earnings alone

• reforms are needed to replace fuel duty receipts which are being lost as drivers switch to electric cars

• increased investment in public services would counter a drop-off in productivity

• the impact of the Iran war has probably reduced the government's headroom against the current fiscal rules from £23.6 billion in March to £10 billion now.

($1 = 0.7464 pounds)

(Writing by William Schomberg; editing by David Milliken)

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