The UK did in lower their records by 5,000. However the reason was not bad record keeping as claimed above. In England the tally included anyone who has tested positive for COVID-19 and later died, with no cut-off point between positive test and death. While Scotland only counts deaths that occur within 28 days of a positive test.

Their official statement is here:
https://publichealthmatters.blog.gov.uk/2020/08/12/behind-the-headlines-counting-COVID-19-deaths/

Classifications should be done as follows:

"A death due to COVID-19 is defined for surveillance purposes as a death resulting from a clinically compatible illness, in a probable or confirmed COVID-19 case, unless there is a clear alternative cause of death that cannot be related to COVID disease (e.g. trauma)."

https://www.who.int/classifications/icd/Guidelines_Cause_of_Death_COVID-19.pdf