Nationals of Taiwan holding passports with National ID number can also apply for the ETA but solely through one of the approved travel agents in Taiwan or an Australian visa office outside Australia. Citizens of Andorra, Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Liechtenstein, Luxembourg, Malta, Monaco, Netherlands, Norway, Portugal, San Marino, Spain, Sweden, Switzerland, the United Kingdom (British Citizens and British Nationals (Overseas) only) and the Vatican City may also apply for the ETA instead of eVisitor but solely through a travel agent, airline, specialist service provider or an Australian visa office outside Australia.

Can we conclude that do british citizens need an eta for australia?
yes