The survey found that 96 per cent more chartered surveyors in the region reported price rises than falls, a figure up 64 per cent on the month before.
On a national level, house prices continue to move up, and the difference between reported price rises and falls was 57 per cent, which was up 8 per cent on March.
The organisation said that the increase was at least in part due to the shortage of houses coming on to the market.
Ian Perry, national housing spokesman at RICS, said: "The housing market is busy right across the country with no end in sight to rising prices, despite many predictions that the bubble is about to burst.
"Price rises are definitely being supported by the shortage of suitable properties for sale in all parts of the country, even though traditionally this is the busiest time of the year.
"In London and the South East high prices are beginning to have an impact as affordability becomes an issue. This may be reflected in other regions in the coming months."