According to the ballpark, approximate data from the online competitor analysis tool Semrush.com, 6/10 of the top UK PR agencies by fee income are not ranking in the top 10 on google.co.uk for any service-related core key phrases (i.e. non-brand related searches).
In short, many of these companies do not seem to understand / place great importance on optimising their online visibility and thus could be doing more to optimise their respective online presences. They may also have had Google take action on their sites for a variety of reasons including the Google 'Panda' and 'Penguin' updates - I have not done an analysis of this. For example, it appears seems the Brunswick Group would benefit from segmenting content for each target market (e.g. US, UK etc) on the site and creating a multi-regional and multilingual site: https://support.google.com/webmasters/answer/182192?hl=en.*
*Google is not the dominant search engine in all of their markets, nor is English the only language people who search for their services will use on search engines in these markets.
** From semrush.com June 2015 data
Based on http://www.prweek.com/abr2015/uk150
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