The report, by the Bradford and Bingley Estate Agents, shows that 96 per cent of sellers are achieving the wanted price for their homes, while average house prices are 7.5 per cent higher than last year.
It is the latest in a string of recent reports that point to a strong housing market already buoyed by low interest rates and increased confidence in both the housing market and job security.
Demand is so strong in the south east, that the average selling time for a home in Luton, Bedfordshire, Loughton, Essex and Sutton, Surrey, is now just one week.
The survey says that almost one third of all properties nationally are selling in three weeks or less.
But the demand has created severe housing shortages, which in turn have led to increased competition for buyers.The shortage is at its worst in the South East where 11 people are looking to buy each home, with the problem increased as people wait to find a property they like before putting their own up for sale.
Other property hotspots include Newmarket, Alton, Brighton, Portsmouth, Glasgow (West End), East Kilbride and Ayr, the report says.
Market towns with good commuting links are also proving popular. Homes in Clitheroe in the Ribble Valley and Yarm in Cleveland are sold within one month.
The Scottish housing market has also reached record levels with homes selling in eight weeks - three weeks less than the average last year. Nationally, it takes 12 weeks to sell a house, one week less than at this time in 1998.
Managing director of David Woodcock, Bradford and Bingley Estate Agents, predicts the levels of activity will decline slightly during the second half of the year.
He added: "On the assumption interest rates will remain low for the foreseeable future, we envisage that the new millennium will have a positive effect on the housing market."
The Department of Environment, Transport and the Regions and the Lord Chancellor's Department are currently considering responses from the housing industry and trade bodies on a consultation paper designed to speed up the buying and selling of homes.
The Key to Easier Home Buying and Selling was drawn up last December and housing representatives were given until March 31 to offer their recommendations.
The departments will announce any changes to the plans during the summer. Nodate has yet been confirmed.Reuse content