I am both a British citizen and a Canadian citizen I live in the UK and only have a British passport. Will being Canadian with proof of Canadian citizenship alter the requirement to obtain an ESTA before travelling to the USA from the UK on a UK pasport?
The US ESTA website says explicitly:
citizens of Canada who are traveling with a Canadian passport do not need an ESTA. (emphasis mine)
I would deduce that without a Canadian passport you will need to go through ESTA.
I'm also a dual British/Canadian citizen, resident in Canada, and I found it well worthwhile to get a Canadian passport precisely to avoid this sort of thing at the US border. But I go to the US pretty frequently.