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LONDON, March 30 (Reuters) - The pound held steady on Thursday, and was heading for its biggest monthly gain versus the dollar since November, as an apparent abatement in concern among investors over the banking sector drove flows away from the U.S. currency.

Sterling has risen by nearly 3% against the dollar in March and is hovering around eight-week highs.

Data this week showed UK grocery inflation hit a record high of 17.5% in March. Temporary shortages of certain food items, such as salad ingredients, helped drive the rise. But overall, at more than 10%, headline inflation in Britain is showing no signs of slowing down.

Sterling was last up 0.4% against the dollar at $1.2361 and up 0.1% against the euro at 87.97 pence. The pound is heading for its largest monthly gain since a 5.2% rally in November. Against the euro, it has been a lot more measured, having barely moved month on month.

"In a similar situation to the euro, the pound is being supported by central bank divergence. The Fed appears less certain about its next step even after the banking sector turmoil seems to have been contained," City Index strategist Fiona Cincotta said.

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"Meanwhile, BoE Governor Andrew Bailey has said that the central bank may need to hike rates again after UK inflation unexpectedly rose to 10.4% in February and food inflation rose to a record high in March," she said.

A report from the BoE on Wednesday showed the volume of mortgages approved by British lenders rose more than expected in February, which suggests the housing market downturn may be levelling off.

Expectations for what the BoE is likely to do this year in terms of monetary policy have changed drastically in March.

At the start of the month, markets were factoring in the probability that UK rates would peak close to 5% by the end of this year - which at that point, meant another 75 basis points in rate rises.

Four weeks on and money markets show traders now think rates will top out at 4.5% by September - meaning they believe the BoE has one more quarter-point rise up its sleeve, at most.

Even with this loosening of expectations, the pound has gained ground against the dollar. The strength in sterling is less about anticipated rate differentials and more about investors releasing their grip on typical safe-haven assets like the dollar, as the acute concerns about the stability of the banking sector have ebbed.

The difference between the yield on 10-year gilts and 10-year U.S. Treasuries is set to rise for the first month since September in March, which gives the pound something of an edge.

Also, daily sterling charts show the technical picture is generally favourable.

"For the moment, the price remains above the 50-day simple moving average, and as long as this remains the case, then the bullish view continues to hold sway, and we expect additional upside above the January highs in due course," IG strategist Chris Beauchamp said.

Editing by Alison Williams