What percentage of UK companies survive?

The register itself answers "what fraction of companies make it": every incorporation and every dissolution since 1980 is on record.

Our survival statistics page charts, for each incorporation year, how many of that year's companies are still active today — measured from the live register weekly, not sampled. Each company page also shows its own incorporation-year cohort ("of companies incorporated in 2015...").

Official sources

The ONS publishes business demography statistics (births, deaths and survival of UK businesses) at ons.gov.uk — methodologically different (it counts trading businesses, we count registered companies), and both are worth reading.