Originally Posted by
corporate-wage-slave
Just use the UK one to enter the UK, you are not subject to immigration controls as a UK Citizen, which as a Canadian you would be. With the e-gates now valid for Canada it wouldn't make a huge difference, so if your UK chip doesn't work and you used the Canadian passport then it's not a big deal. There is no requirement to stay consistent with your Advance Passenger Information in this scenario. For the Helsinki trip, if you stay airside then there is no passport check for immigration purposes at LHR.
I have exactly this - my UK chip ceased working many years ago and if the queue to see a person is lengthy I simply use my US passport at the LHR e-gates. I don't do this very often as I don't typically take my US passport anywhere other than America, but nobody has knocked at my door yet and I believe that I am currently "American" if you see what I mean.
I think someone already answered this but if you are dual US/UK travelling to America, you are not getting on the plane without showing your American passport. This presumes that dual citizens don't apply for ESTAs on their UK passport of course, but in any event I believe dual nationals have to enter the US using their American passport.