Yep, assuming you’re not a single pensioner living in a 5 bed house (or in some areas of the South East of England), although you’d get a significant discount on Council Tax if that’s the case and clearly most in that situation would have other savings or other pensions.
IFS website
“Around 74% to 80% of pensioner households in the UK own their homes outright, meaning they live mortgage-free. Only a small fraction (around 4%) are still paying off a mortgage, while the remaining pensioners rent privately or live in social housing”