According to an article on The Lawyer's Website which lists the Top 20 law firms in England based on a branding survey where…

The researchers maintained that those at the top had separated themselves and had “the best reputation” in brand terms. They said the table was based on a combination of press coverage, social media activity and “front of mind responses from the wider industry”.

The Top 20 list follows with links to each of the firms' Websites.

The Top 20
1 Allen & Overy
2 DLA Piper
3 Eversheds
4 Irwin Mitchell
5 Clifford Chance
6 Linklaters
7 Withers
8 Pinsent Masons
9 Herbert Smith Freehills
10 Freshfields Bruckhaus Deringer
11 Pannone (to merge with Slater & Gordon in February 2014)
12 CMS
13 Hogan Lovells
14 Ashurst
15 Taylor Wessing
16 Olswang
17 Norton Rose Fulbright
18 Slaughter and May
19 Addleshaw Goddard
20 Berwin Leighton Paisner