It's got nothing to do with the UK Identity and Passport Service. It's entirely at the discretion of the Bolivian immigration service as to whether you can be admitted.
From The Guardian website:
"The number of remaining blank pages a passport should have is also an issue. Some travellers have reported arriving with one or less than one full page left and waiting for hours at immigration, until an official reluctantly grants them entry. The FCO lists no hard and fast rules because, in many cases, there aren't any."
and
"A home office spokesperson said: "If you are going to a country where you need a visa, you should find out during the application process how many blank pages you need." "
http://www.theguardian.com/travel/2013/jun/20/passport-expiry-dates-blank-pages
The only information given on the website of the Bolivian Embassy is that your passport needs a minimum of 6 months validity on it:
http://www.bolivianembassy.co.uk/visas_turismo.html
(There's no reference to blank pages).
So try an email to:
[email protected]
or phone 0207 235 4248