Approximately how many takeaways, restaurants, cafes, and pubs that
serve food are there in the UK?

I already know of websites such as thefoodplace.co.uk and
topmenus.co.uk which provide a limited subset of these establishments,
but they do not cover all by a long shot, although they may provide
help with research.

If possible, broken down into categories,though I appreciate this may
not be possible.

e.g. (pulled out of the air): 

15,000 Chinese takeaways,
14,000 Indian takeaways
13,000 Pizza / Burger / Kebab shops
12,000 Pubs that do food 
11,000 cafes

etc

Something along those lines, along with links to sources and how you
acquired the information would be great. Good luck!

2004 Provisional Stats

Restaurants 26148
Quick Service 29566
Pubs 51249

Source: http://www.outofhome.org/o_trends/foodservice_intell_data.pdf

Realize this doesn't answer the question but it is a piece of the puzzle.

Thanks canadianhelper-ga.

That's definitely along the right lines, if it could just be expanded
to split the Restaurant / Quick Service section into categories
(Chinese, Indian, Italian, etc) it will be perfect. I don't need it
exact of course, but as long is it is approximately correct, hopefully
with a reference like you just provided then I will be more than
satisfied.