* March CPI rate falls to 4.0 pct from 4.4 pct in Feb
* Inflation fall puts BoE May rate rise in doubt
* Retail sales show worst drop in at least 16 years in March
* UK trade deficit narrowest since Feb 2010
(Adds context, wraps in BRC retail sales data)
By David Milliken and Peter Griffiths
LONDON, April 12 (Reuters) - British inflation eased in March for the first time since last summer as grocers cut food prices, providing the Bank of England with fresh leeway to hold interest rates steady to support the still shaky economy. The unexpected drop in annual inflation to 4.0 percent from 4.4 percent in February -- together with a sharp decline in retail sales -- gives ammunition to those policymakers who want to see the economy on a solid footing before tackling inflation.
Sterling fell and gilt futures extended an earlier rally that had been driven by speculation about a soft inflation number.
"It should help to stave off a rate rise in May," said Philip Shaw, an economist at Investec. "But while this is welcome, this is just one battle in what will be a long tussle. It's still possible inflation will rise to 5 percent over the course of the year."
The fall in the CPI rate last month was aided by a non-seasonally adjusted 1.4 percent month-on-month drop in the cost of food and non-alcoholic drinks, which the ONS said was driven by supermarket discounting.
HIGH STREET WOES
The BoE faces a dilemma as it tries to tame inflation -- still at twice its 2 percent target -- without derailing a fragile economic recovery after the economy contracted at the end of last year.
Britain's high street is suffering from a poisonous mix of a rising cost of living, higher taxes and downbeat consumer morale, and business leaders urged the BoE to stay away from raising borrowing costs too soon.
The British Retail Consortium said total sales, a measure which includes new floorspace, fell by 1.9 percent in March , the worst drop since the BRC began collecting the data in 1995. Like-for-like sales were 3.5 percent lower on the year.
"This is strong evidence of the pressure customers and traders are under," said BRC Director General Stephen Robertson. "Uncomfortably high inflation and low wage growth have produced the first year-on-year fall in disposable incomes for 30 years."
The trade body urged policymakers to delay raising rates, saying a hike "would do more harm than good".
Companies such as Dixons, Britain's biggest electricals retailer, electricals group Kesa, carpet seller Carpetright and car parts retailer Halfords have warned about the tough outlook.
GROWTH
The sales slump came on top of a recent suprise drop in industrial production and a weak rebound in construction in February, casting doubts about the strength of the recovery.
Consumer price inflation has been above the Bank of England's 2 percent target since December 2009, driven higher by a mix of a weak exchange rate, rising commodity prices and two successive annual increases in sales tax.
Last week, the BoE opted to hold rates at a record low of 0.5 percent, breaking step with the European Central Bank which raised the cost of borrowing for the first time since the 2008 financial crisis.
Economists say the majority of policymakers who voted for steady rates in past months would want to see a strong economic rebound before tightening policy.
"We suggest a GDP figure of around 1 percent quarter-on-quarter and PMIs in excess of 55 would be required to get a majority in favour of a very modest hike," ING analyst James Knightley said.
In some good news for the economy, separate ONS data showed that Britain's trade deficit for goods and services fell to its smallest level since February 2010. That suggests net trade will provide a bigger contribution to first-quarter GDP figures due later in April.
The ONS said that Britain's total global trade deficit fell to 2.443 billion pounds ($4 billion) in February from 3.858 billion pounds in January, driven by an unexpected fall in the deficit for goods.
Manufacturers have reported stronger exports for several months, but this has been slow to show up in official data. (Editing by Stephen Nisbet)