Forestry is a devolved matter and so this answer is in relation to England only.
The Government does not have a statutory duty to collate numbers of Ancient and Veteran Trees. The Ancient Tree Inventory (ATI) currently lists 160,000 ancient, veteran and notable trees across the UK. The Natural England and Forestry Commission Standing Advice on Ancient Woodland, Ancient and Veteran Trees, available at https://www.gov.uk/guidance/ancient-woodland-and-veteran-trees-protection-surveys-licences, directs users to the Woodland Trust’s ATI which is collated by volunteers around the country at https://ati.woodlandtrust.org.uk/.
The Government updated the National Planning Policy Framework in 2019 to improve protection of ancient and veteran trees, noting that these are irreplaceable habitat and these should only be lost to development with wholly exceptional reasons and with a suitable compensation strategy in place. For more information you can visit https://www.gov.uk/government/publications/national-planning-policy-framework--2.