UK Consumer Price Index since 1988

Consumer prices index, CPI, is the government's preferred measure of inflation, it corresponds with inflation measures used by other European countries, it used to be called Harmonised Index of Consumer Prices. It excludes mortgage interest payments and council tax. It is the most widely-publicised measure of inflation.

Retail Price Index, RPI, is a familiar and long-established measure of cost-of-living in the UK. It includes mortgage interest payments and council tax. But since 2010 it has been overstating inflation. In 2012/2013 statisticians at the Office for National Statistics confirmed that the formula used to calculate parts of the index had overstated inflation.
Despite this RPI is still used in some wage agreements, commercial lease agreements, regulated rail fares and index-linked government bonds. Many final salary pensions are linked in-full or in-part to RPI. Since 2012 student loan interest rates have been linked to RPI (good grief).

CPIH is Consumer prices index, CPI, plus owner-occupied-housing-costs and council tax. An updated CPIH was relaunched in February 2017 with estimates back to 2005. It is promoted by the Office for National Statistics(ONS) as 'the most comprehensive measure of inflation'.
Since 2008 inflation of mortgage-payments, has at times been less than CPI inflation so CPIH has often been lower.
Roughly 10% of CPIH is owner-occupied-housing-costs.

Back in January 2015, the Institute for Fiscal Studies, a research organisation not linked to the government, estimated that indexed-linked gilts were costing the taxpayer an additional £2bn per year because they use RPI.
On July 20, 2017 Chris Giles Financial Times economics editor raised this issue again. There are £407bn index-linked government bonds linked to the RPI.
Apparently for 94% of UK index-linked gilts there is nothing which says the Government cannot change the index to which they are linked. If RPI were abandoned the bond-holders must accept "an officially recognised index measuring changes in the level of UK retail prices", for example CPI.
For the remaining 6% who hold three remaining issues sold before 2002, the government would have to inform them and offer to redeem their stock at par. The market value of these issues is £67bn and the redemption value is £49bn. So nothing much would happen.
On January 30 2018, Bank of England governor Mark Carney speaking to a House of Lords economic affairs committee called for a "deliberate and carefully timed" withdrawl of RPI from use in government contracts because "most would acknowledge the RPI has no merit".
Index-linked bond contracts link their annual uplift to the RPI and the ONS is obliged by law to produce the index every month, the only named statistic British law requires the ONS to produce.