I am curious as to how long restaurants survive, on average.  I have
heard quotes anecdotally, but I have never seen anything based on real
data.  I am a food writer living in the UK, so UK data would be best,
but I would be interested in geneuine data from elsewhere e.g. the
USA.

I am unsure if this will be of much help, but I thought I'd mention it:

"In a study in Columbus, Ohio, Professor H.G. Parsa of Ohio State
University, tracked new restaurants from 1996-1999. In the first year,
26% closed. Another 19% closed the second year, and 14% the third.
Collectively, 59% of new restaurants closed those three years. By the
way, the "failure" rate wasn't very different between franchised
restaurants ? 57% ? and independent restaurants ? 61%."

http://www.usatoday.com/money/smallbusiness/columnist/abrams/2004-05-06-success_x.htm

Have a good day.

Plenty of comments from the US surrounding this piece of research but
not much on the UK.
http://researchnews.osu.edu/archive/restfail.htm

The best reliable information I can find is contained in the VAT
survival rates but these lump hotels and restaurants to together, and
of course, does not included non-vat registered establishments.
http://www.sbs.gov.uk/sbsgov/action/layer?r.l2=7000000243&r.l1=7000000229&topicId=7000011767&furlname=survival&furlparam=survival&ref=http%3A//64.233.161.104/search%3Fq%3Dcache%3AcX1HASXSqJEJ%3Awww.sbs.gov.uk/SBS_Gov_files/researchandstats/VATSurvivalRatesKeyResults.pdf%2Crestaurants%2C%2522survival%2Crate%2522%2Cuk%26hl%3Den%26gl%3Duk%26ct%3Dclnk%26cd%3D1&domain=www.sbs.gov.uk

I think that failure percentages (like the ones Thither gave) will be
your best statistics on this matter.
I ate in a restaurant last weekend in Connecticutt that was opened in
1860.  I don't imagine it will be closing down anytime soon.  The
chance that such restaurants could potentially live forever will make
any real statistician think 2ce about attempting to calculate the mean
number of years a restaurant stays open... the median however could be
calculated and is somewhere around 2.5 years according to
Answerfinder's first link.