The agency has this month adopted a new statistical method for calculating prices. It puts the average at £145,455, up from £141,918 in April last year but still below the peak of £155,738 in October 2007 before the financial crisis.
Within Cumbria, Copeland saw the sharpest increase in average prices, by 7.3 per cent to £115,150, followed by South Lakeland, up 2.6 per cent to £217,373, Allerdale, up 2.5 per cent to £143,149, Carlisle, up 2.2 per cent to £130,705, and Barrow, up 1.4 per cent to £102,736.
Eden was the only district where prices fell, by 1.2 per cent, to £182,151.
The Land Registry figures also show that the number of homes being sold remains constant. An average of 573 changed hands each month between December and February, compared with 569 in the same period of 2014-15.
Nationally, prices rose by 8.2 per cent in the year to April taking the UK average to £209,054. London saw the steepest increase, 14.5 per cent, while prices in the North East barely increased at all.
* Inflation was unchanged last month, the Office for National Statistics says. The Consumer Prices Index (CPI) stood at 0.3 per cent as higher transport and eating out costs were offset by sliding clothes and food prices.
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