The figure for the cap is actually £86k, not £81k.
Further, it's extremely misleading, as it only refers to the costs of actual 'care' and NOT to the costs of accommodation within a care home, nor any associated costs, such as those for food. It's also worth noting that the cap only applies to those regarded by their local authority as being eligible for it, which is likely to exclude all but the most frail anyway.
See here
https://www.hughjames.com/blog/what-does-the-86000-cost-cap-actually-mean
and here
https://www.bbc.co.uk/news/health-58442991