How can British retirees use their pension to meet the sufficient income requirement to gain residency in Italy?

You should not confuse the Elective Residence Visa with the Investment Visa. The Elective Residence Visa is for those who want to live in Italy without working and requires the applicant to have a minimum passive income (i.e. not deriving from work or salary) of at least 31,000 euros per year and to have a suitable accommodation. You just need to prove that you have a pension above the minimum threshold and this can suffice to obtain the visa, but consulates keep some discretion in issuing it despite you meet the minimum requirements. An Investor Visa can be obtained by purchasing 2 million euros in Italian government bonds (to be kept for a period of at least two years); or by investing 500,000 euros in a company, or 250,000 euros in an “innovative start-up”; or by donating 1 million euros in philanthropic projects of public interest. For this visa, you will need to do the actual investment within 3 months of entry into Italy.

You should not confuse the Elective Residence Visa with the Investment Visa. The Elective Residence Visa is for those who want to live in Italy without working and requires the applicant to have a minimum passive income (i.e. not deriving from work or salary) of at least 31,000 euros per year and to have a suitable accommodation. You just need to prove that you have a pension above the minimum threshold and this can suffice to obtain the visa, but consulates keep some discretion in issuing it despite you meet the minimum requirements. An Investor Visa can be obtained by purchasing 2 million euros in Italian government bonds (to be kept for a period of at least two years); or by investing 500,000 euros in a company, or 250,000 euros in an “innovative start-up”; or by donating 1 million euros in philanthropic projects of public interest. For this visa, you will need to do the actual investment within 3 months of entry into Italy.