There is a problem: As a Cdn, you require nothing but passport to visit US. However, absent a Cdn passport, you will need to carry your
UK passport. UK citizens fall under the Visa waiver program (which means you don't need a visa), but also subjects you to ESTA.
This, the problem with having only british passport is that you may fall under the ESTA program, whereby those not requiring visas, must pre-register and pay a fee.
https://esta.cbp.dhs.gov/esta/See, Cdns are exempt from ESTA, but Cdns are also required to show their passport. It would be up to the CBP if they would admit you "as a Cdn" rather than a UK citizen.
Your best bet is to follow up with ESTA. Your question will be: Is a Cdn citizen with a British passport considered Cdn or British? if cdn you are good to go. If british, you will need to do ESTA.
http://www.cbp.gov/xp/cgov/travel/id_visa/esta/