The forecast predicts prices will rise by 7.4 percent this year and 7.2 percent next year, easing back to 4.2 percent in 2016 as the mortgage guarantee scheme ends.
EY said the financial services watchdog, the Financial Conduct Authority (FCA) will play a crucial role in keeping a lid on prices and newly gained abilities to rein in lenders must be used.
Read MoreAverage London house double UK average at $750,000
"The FCA will assume crucial importance to ensure multiples do not become too stretched and that affordability is scrupulously checked. If these controls are rigorously applied this will eventually constrain London prices," said Peter Spencer, chief economic advisor to EY ITEM Club.
However, this forecast is at odds with other surveys, which suggest there will be consistent price rises in the next five years, fueling fears the market is in serious bubble territory.
Read MoreUK inflation sinks to 4-year low, house prices surge
U.K. house sales hit a six-year high in March, the Royal Institution of Chartered Surveyors (RICS) study revealed on Thursday, and a supply shortage will continue to send prices soaring, with RICS expecting property prices in Britain to rise 6 percent yearly over the next five years.
As recent as last month three pillars of the British establishment, the Bank of England, the Office for Budget Responsibility (OBR) and a member of the British royal family warned of a housing "shock", with heir to the throne, Prince Charles warning the average London house price will have risen 40 percent to £650,000 ($1.08 million) in six years' time.
Read More Royal family, Bank of England warn of housing 'shock'
The EY forecast was also positive on the U.K. more generally, as it expects to see growth of 2.9 percent this year. The group is also eyeing an interest rate rise in the third quarter of 2015, at which point it expects interest rates will rise gradually.
Business investment is also set to strike back, with growth hitting 9.1 percent this year and unemployment will fall in line with Finance minister George Osborne's predictions. That could mean the U.K. may overtake Germany as having the highest rate of employment in the G7 by 2017, the group said.