I need a white paper or discussion document writing that gives,  
  
An overview of the UK Prof Services sector (Business Services,
Lawyers, Accountants, Consultancies, etc;), eg size of market, no of
employee's, no of companies, Top 20 companies (by Fees or Mkt Cap), 

A potted history of how they've evolved with specific focus on the last 5 years
or so, the places they are feeling pain (and success) at the present
time, and where they see their key opportunities for growth over the
next 1 - 5 years.  
  
And secondly how these companies view the impact of mobility on their
businesses. More specifically what is the opportunity for the Wireless
network operators in this space in terms of their business activities,
this needs to cover the effect wireless mobility will have on their  
internal business practice or culture (eg remote working) and how they
interact with their customers from a revenue genaration and customer
expirience perspective.

As I suspect you know, the information you're looking for is usually
available only in market reseredarch reports that cost from hundreds
to thousands of dollars - EACH -- and you're looking for a lot of
industries!

I would be more specific about the list of industries - "etc." doesn't
help much. For instance, are private banks included in "financial
services"? "Consulting" about what? Advertising? IT services? How to
sell icecream?

I'm not a Google researcher but I did a quick check in a few databases
and found free executive summaries of several market research reports,
lots of tables giving statistics of various industries in the range
you asked for, etc. If that sort of thing is acceptable it would be a
good idea to say so - if you limit yourself just to "white papers" you
probably won't get anything. Nobody seems to have written them for
you, this time around.

Good luck!