On the year, however, growth was 2.3%, slowing down significantly from 7.6% in March 2016.
In terms of regions, the strongest performance was seen in the Midlands, with East and West Midlands prices at record highs.
Prices in the East Midlands were up 2.1% on the month and 5.7% on the year, surpassing £200,000 for the first time. Prices in the West Midlands were also up 2.1% on a monthly basis, and 4.2% on the year.
Miles Shipside, Rightmove director and housing market analyst said: "Since the start of the decade, the average March price rise has been 0.9%, so this month's 1.3% uplift is an indicator of a shortage of suitable property for sale in many parts of the country, with strong demand for the right property at the right price.
"Since 2007we've only once seen a larger rise than this in March, and we are also keeping pace with last year's rise, which had the added momentum of investors looking to beat the Stamp Duty tax deadline of April 1st."
In London, property prices were up 1.4% on the month and 0.9% on the year to £649,772, driven mainly by increases in Outer London, where the average price was up 2.6%, compared to a 0.4% rise in Inner London.
Shipside said buyers were looking further afield for value, pushing up demand and therefore prices in many outer boroughs.
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