The pair have added some celeb-bashing bite to their Very Important People series, which pokes fun at Natalie Cassidy, Frankie Boyle, Adele and dozens more.
Digital Spy caught up with the duo to talk about their inspirations, Peter Andre's jumpers and how one of them used to think they were "a horse".
Do you hope this show can revive British TV audiences' love for impression shows?
Terry: "No, we're hoping to bury it. We're hoping to be the final nail in the coffin!"
Impressions do have a bad rep these days though...
Morgana: "They've all become a bit BBC really. They're all a bit jazz hands and there's no message. There's no message or story. It's just, 'I'm being so-and-so'. And that's it. With this, I think there's a modern message."
Terry: "To be fair, Dead Ringers was massive. It was a big hit and it ran its course. It had a big ensemble cast so that worked. I think impression shows can struggle when it's one person in the lead and there's nobody else to rely on. The whole show is governed by that one person's talent."
Morgana: "Some impressions have been good as well. I think it's unfair to be mean about them all. Stella Street was good and Star Stories was very funny."
Terry: "I think Star Stories worked because it did its own thing. It didn't care about the impersonation, it just wanted to be funny. Being funny is better than technical brilliance."
I've seen the first 20 minutes of episode one...
Terry: "You should do another 3 minutes, it's only 23 minutes long! We mention you at the end and you missed it. It was brilliant."
Morgana: "You shouldn't have run off to get pissed."
It feels like you're more interested in making a comedy show rather than perfect impressions; is that right?
Morgana: "Oh God yes. You've got to make these characters your own. There's no fun in copying."
Terry: "You would go mental trying to replicate people sound for sound. Something so hardcore would drive you mad. After a while, you've got to take it and make it stupid."
Are you worried about the response of the celebs? Especially someone like Frankie Boyle?
Morgana: "I am fairly certain Frankie Boyle couldn't give a flying f**k. If he's sat at home going, 'Oh my God!' I'd be a bit like, 'Really?' We barely touch him. He goes around making jokes about Jordan's kids."
Terry: "You've got to be very thick-skinned to be a stand-up. It won't be the first time that someone has hollered something at him, that's for sure. And even if he is offended, we're in so much make-up in this show, we can hide in the darkness. We'll hide in the alleys. I'm a wall!"
Did you both grow up doing impressions?
Morgana: "I thought I was a horse until I was about 12."
Terry: "I used to do my maths teacher at school. It all stemmed from there."
Morgana: "I would take the piss out of the science teacher and stuff like that. But the funny thing I found out only the other day was from some girlfriends of mine; apparently I used to do impressions of Natalie Cassidy as Sonia in EastEnders when I was at school. I must have blocked that out of my mind."
Terry: "Blocked it out like a car crash."
Morgana: "I have Sonia from EastEnders whiplash."
Watch the trailer of Very Important People:
How do you decide who you will do?
Morgana: "Eeny meeny miny mo. How do we do it? I think it's fairly random who we pick. It's a bit like Take Me Out."
Terry: "We want to make a show in its own right and it's not Terry and Morgana's best impersonations. We want to make a funny show, not just, 'Here's my David Attenborough for half an hour'. We wanted to create characters and morphs rather than cast iron impersonations. We wanted current celebs like Joe Swash and Natalie Cassidy. When you crowbar in an old film star everyone goes, 'What the f**k?' We wanted it to be topical and we wanted it to be original."
Who didn't make the cut?
Terry: "I thought my Jamie Oliver was going to make the cut, but I sat through producers and directors saying, 'nope'. Everything went quiet. It's hard to tell when you do it alone. You drive yourself a bit mental. My first Jonathan Ross started out like Fagin and it went more olde world Jewish as I went along."
My favourite sketch involved Joe Swash and Stacey Solomon in 'Facebook: The Musical'....
Terry: "That came from my despair sometimes with the West End. When you walk past and see some shows and you think, 'How did they come up with that?' I wish the West End had more ideas of its own. I remember when I first heard about Mamma Mia and I thought, 'What on earth is that about?' And it is a bit ridiculous. 'Where shall we get the train from chaps? Oh, how about, 'Waterloo'... doo-do-dooo'. Really tenuous links to get into stuff."
Why do people find impressions so funny?
Morgana: "I don't really know. I do think there's an immediate satisfaction to these shows. There's an escapism to impressions and combined with the obsession and cult of celebrity - this fast food-like, almost religious love of celebrities - the show just works. People don't need to spend time learning about characters they don't care about."
Terry: "On that One Born Every Minute, there's a moment with Myleene Klass. I love that show and the doctors and nurses are incredible, but Myleene Klass appears and these people go mental. It's crazy. I guess it was the same in the '60s when celebs went places, people sat up and took notice, but I just think things have gone further with people like Joe Swash and Pete Andre. Joe Swash buys a Mars Bar - read all about it. Pete Andre on his telly show buying a new jumper. 'Oh man I need a jumper,' says Pete Andre. The voiceover man says, 'Peter needs to buy a new jumper'. And by the end of the episode Peter Andre has a new jumper. You just sit there and think, 'What the f**k am I watching?'"
Right, I'm off to watch the final three minutes!
Terry: "Do it! It will be a lesson in dedication for you. Life will come easier. When people ask you what the film was like, you won't say anymore, 'Oh I don't know. The last three minutes I simply couldn't be bothered with!'"
Very Important People airs tonight (April 27) at 9.30pm on Channel 4