No, you do not need a transit visa.
You don’t need a visa if you have one of the following:
- a visa for Canada, New Zealand, Australia or the USA (this can be used for travel to any country)
Check if you need a UK visa
You can see what options I chose in the visa check flow to get that answer, please ensure that my choices were correct (especially the “will you need to leave the airport” one, as that slightly changes the outcome).