 In 1952 Parke was a founding member of the British Phycological Society, edited The British Phycological Bulletin (1967–1967) and was President of the Society from 1959 to 1960.Parke was awarded international honours including Corresponding Membership of the Royal Botanical Society of the Netherlands (1970), Membership of the Norwegian Academy of Science and Letters (1971), and the Fellowship of the Royal Society (1972).In addition she was a Fellow of the Institute of Biology and the Linnean Society and was awarded an honorary Doctor of Science degree by the University of Liverpool in 1986.