The gatherings, first reported by The Telegraph, took place on 16 April 2021 and went on until the early hours.
The prime minister's spokesman said it was "deeply regrettable that this took place at a time of national mourning".
Boris Johnson was not at either party - but he faces questions over alleged Covid rule-breaking at No 10.
The latest party revelations led to a backlash from opposition parties, who contrasted the behaviour of No 10 staff with pictures of the Queen sitting alone at the Duke of Edinburgh's funeral, due to Covid restrictions.
