Britain’s biggest property website has rebuffed claims that the housing market is heading for a slowdown, with a forecast that prices will soar by 30% over the next five years to average £318,000 in England and Wales and more than £715,000 in London.

But for the first time in more than a decade, it will be markets outside the capital that lead the way in price rises, Rightmove said. It predicts that Southampton will see the fastest house price increases in the country, with values expected to jump 43% by 2019 – adding nearly £100,000 to local prices – while Luton, Brighton and Swindon will not be far behind. Rightmove used independent consultancy Oxford Economics to calculate the figures.

The driving force for prices in the south-east will be the “spillover” effect of high London prices rippling through the home counties. But Rightmove said the parts of the capital that have seen the greatest price increases in the last five years will see the smallest in the coming five years.

It predicts price growth of 13.6% in well-off parts of west London, and it names Enfield in north London – until now one of the cheapest property areas in the capital – as the borough that will see the biggest gains. It said average prices in Enfield will rise from £381,000 to £531,000 or 39% – equal to an increase of £575 every week for the next five years.

The prospect of house prices rising at the rate forecast by Rightmove will put homes further and further out of the reach of first time buyers. It said the average price in England and Wales will rise from £244,192 to £317,967 – a gain of £73,775 or £14,755 a year.

The report claims to be “the most comprehensive house price forecast of its kind ever created, based on property and economic data rather than opinion and short-term market factors. It takes into account both asking and sold prices, surveyor valuations and analytics from the Oxford Economics’ global, industry and regional forecasting models.”