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Not at all. There's a cadre of people who enjoy British television programming in America, but they don't count. I'd estimate that the number of people that have watched for example the UK office is maybe 1% or less than the people that watched the US office in the US.
You wouldn't have look very hard to find an American who has seen Downton Abbey, Doctor Who, or Bake Off. The biggest problem keeping Americans from watching UK TV is access, not some inherent dislike or disinterest in compelling television whenever British people are involved. A show has to be wildly popular before Americans even get the chance to be exposed to it, which really limits the amount of viewers for UK pr…
For anyone unfamiliar Graham Norton hosts a late night style talk show but instead of inviting guests out one by one and talking to each in turn he brings them all out together. He still focuses in on each guest at times but he jumps between and encourages them to engage with each other like a good dinner party host. Here's an example of British comedian Greg Davies telling a story while Ryan Gosling next to him dies of laughter: https://www.youtube.com/watch?v=yuXGpUR7fXA
It essentially copies the best parts of panel shows and since he started doing that a lot of folk (most notably Jonathon Ross) have started to copy.