If you have access to the Gale Primary Sources database, there are many newspaper and journal references to the HMS Hawkins including in the time period you mention. eg in the "Malay Mail", "The Times of Malaya and Commercial Advertiser of the Federated Malay States and Straits Settlement", "Straits Echo and Times of Malaya", as well as British newspapers eg "The Times". Also some monographs eg "Shanghai Municipal Council. Report for the Year 1925" there is a mention of a boxing match between 8 students of the Public School for Boys and men from HMS Hawkins.
Gale Primary Sources can be accessed through many libraries - I have access from home through my Australian National Library card.