FT.com do a very good weekly news summary which you can get emailed to you every Friday morning. Although it's the FT, the news tends to be a mixture of national news and big business news.
The Guardian website has a very good daily service, which rouonds up all of the major stories as featured in every national newspaper. There are also links to other online papers, as well as 'headline of the day' and sports news. The service is called The Wrap, and you can sign up at www.guardianunlimited.com