Should the comma be inside the closing inverted commas, in British English?

“I am sure Mahathir will help to place a candidate (against Anwar in a by-election) and that is for sure.

“Mahathir will go all out to ensure Anwar doesn’t become prime minister”, Lokman was quoted saying by Malaysiakini.

Lokman said if Dr Mahathir’s effort to prevent Anwar from winning the by-election failed, it would mean the start of Pakatan Harapan’s downfall.

Should the comma be inside the closing inverted commas, in British English?

Thanks.