If you have an occupational pension, which is a private pension you have no choice over what annual index is used, nor, for most of us drawing an occupational pension any choice over whether to pay into it or not when we were at work.
If you had a personal pension pot that had to be invested into an annuity either on retirement or by one's early 70s at the latest and until recently few people had access to any information or advice to guide their annuity purchase decisions and therefore tended to accept the product their savings vehicle supplied.
To answer the original question. Although they do it, it is quite risky for occupational pension funds to offer any specific annual escalator to its pensioners as the return they make on your money is dependent on the financial markets, interest rates and company dividends and in recent years no only have we seen plummeting interest rates, which is why money invested in annuities produces such a poor income compared with previous years but dividends have also been shrinking. For example BP, Tesco, M&S and Shell used to all be good dividend payers, but are no longer and as large companies with a lot of shares paid a prominent part in any insurance company's or private pension fund's investments.
You cannot and should not make any private pension providers tie themselves by law to any specific index. In times of financial weakness this could bring the pension funds down and destroy the funds that provide many pensioner's income. I saw what happened to a relation whose pension disappeared with Robert Maxwell, the reason was different but the result could be the same
