Prices increased by 0.3% month-on-month across the country, following a similar uplift in March, with a 0.7% rise in London driving the rate of growth, Hometrack found.
Demand from new buyers registering with estate agents in London has grown three times faster than the rate of homes coming on the market over the last three months, the study said.
Meanwhile, some key signs of the health of the London market have recovered to levels not seen since the property boom in 2007. These include the typical proportion of the asking price achieved on London property sales, which now stands at over 95% in both London and the South East, compared with 93% in the rest of the country.
London homes now take just four-and-a-half weeks to sell typically - which is around half the national average and also the quickest selling time seen since 2007.
Although the strength of the London market continues to outperform the rest of the country, there are signs that the market is also picking up elsewhere. This has been helped by improved levels of confidence in the market generally and a continued shortage of homes coming up for sale, according to Hometrack, which questions around 6,000 estate agents and surveyors for its survey each month.
Across the country, the length of time it takes to sell a home has been cut from almost 10 weeks in January to nine weeks by April. Meanwhile, demand from buyers registering with estate agents has been outstripping the supply of homes coming to market for the last three months. Across southern regions it now takes less than two months to sell a house on average, although across the Midlands and northern regions it still takes over 10 weeks, and the average selling time in the East Midlands is 13 weeks.
The North East was the only region across England and Wales to see prices dip month-on-month in April, recording a 0.1% decrease. Prices were flat in the Midlands, the North West and Yorkshire and Humberside. They increased by 0.1% in East Anglia, the South East and the South West and saw a 0.2% uplift in Wales.
Richard Donnell, director of research at Hometrack, said some "noticeable" shifts in the market are helping to bolster house prices. One is that home owners who are considering moving are delaying putting their own home up for sale before they find somewhere to buy. This is in turn keeping the number of homes on the market low and firing up demand.