In 2016, Lindsay MacDonald asked that same question (TV Query):
"I'm very musical, and I can play a little bit, but piano was never my instrument," he tells us. "Hopefully people believe I'm actually tinkling those ivories."
"The singing is definitely me," Ellis clarifies. "The singing is all me."
And from another source (Brittany Frederick for Fansided):
“I’ve never learned to play the piano,” he said. “It’s me singing but it’s not me accompanying myself, let’s put it that way.”
A bit more on his musical background from another interview with Emma Brown in 2015 (Interview Magazine):
ELLIS: My mum was a music teacher. I’ve got three sisters and we all played instruments when we were kids.
BROWN: What did you play?
ELLIS: I started on the trumpet and then I upgraded to the French horn. I played in orchestras my entire teenage years. But, on the drama front, no, not really. My dad, strangely enough for this job, was a Baptist pastor, so I grew up in the church as well. I suppose there is a dramatic element to his job, and he enjoyed doing amateur operatics.