I would be surprised if the uncertainty was much
lower than 1%,

Do you mean 1% (eg CPI of 2.2 +/- 0.022 %) or 1% point (eg CPI of 2.2
+/- 1 %)?

Both are too extreme. The ONS used to reckon that +/- 0.1 percentage
points was about the margin for the year-on-year change but stressed
that that wasn't a "proper" statistical measure. They don't even
publish that now but hope to do somethingsoonish. See eg
cpigandm_tcm77-253092.pdf and
http://www.ons.gov.uk/ons/guide-method/method-quality/quality/quality-information/economic-statistics/summary-quality-report-for-cpi.pdf

And remember ONS make available underlying data so you can always DIY an
index.

--
Robin
reply to address is (meant to be) valid