score:7
According to Rezanov's journal, they spent those days sightseeing and visiting Russian diplomats in London. They visited Westminster abbey, London Tower, Greenwich observatory and Newgate prison, amongst other places.
He doesn't write much about his entourage, save for Horner - expedition's astronomer, who needed to buy his instruments in London. It seems that this was the main reason for visiting London - as soon as astronomical equipment was delivered, Rezanov returned back to Falmouth.
Source: Резанов Н.П. Первое путешествие россиян вокруг света, описанное Н. Резановым / Н.П. Резанов // Отечественные Записки. - № XII; 1824, pp. 25-37 and 328-351, retrieved here (warning, old Russian)