That show is traversing the UK as we speak, and this week they're at London's Wilton's Music Hall, up to and including Saturday, then they'll be back in the big smoke for the Underbelly Southbank Festival in June.
Meanwhile those tour dates also include the similarly self-explanatory Morgan & West's Utterly Spiffing Spectacular Magic Show for Kids & Childish Grown Ups.
"They are both big fun magic shows full of baffling tricks and no small amount of silliness," the time-travelling magicians tell us. "Obviously one is more aimed at children than the other. We'll let you work out which is which."
The question is, if they have a stinker, do they just travel back and play it again?
We did bits and pieces just sort of mucking around for a while, but our first proper gig was at the Queen of Clubs Cabaret in the Isis Tavern in Oxford. We can't recall anyone else who was on the bill, but it was a reasonable crowd of maybe 50 people, and we knocked someone's red wine over them by throwing a stuffed pig into the audience.
We called him Hamdini. He retired soon after that gig. We tried out a new trick we'd just written, that we still perform to this day. So it can't have gone that badly.
Favourite show, ever?
That's very hard to say, we've had lots of really fun shows for lots of different reasons, but the one that sticks in our mind at the moment is last Christmas eve. We were performing our Christmas show - Morgan & West: A (sort of) Christmas Carol Magic Show - in the Oxford Pegasus theatre. The room was full, it was the end of a 34-show run and everyone was just really up for a fun time. It was brilliant, and amazingly still managed to feel quite Christmassy despite how often we had performed the show.
We've played lots of weird spaces, odd crowds and unhelpful environments, but the one that absolutely takes the biscuit was a gig we were booked for as part of a Christmas festival.
We were meant to be doing two half-hour performances during the day, but the night before the entire south of England was blanketed with thick snow, and the journey that should have taken us two hours took six, crawling along an M40 strewn with sports cars stuck in the snow.
When we finally arrived at the gig there was basically no one at the festival, there was no way of getting audience onto the stage, and whilst it was technically undercover the stage was outdoors in sub-zero conditions.
We shivered our way through our set as best we could, performing to 15 people huddled around gas heaters miles from the stage, before cutting our act short for fear of developing hypothermia.
Which legendary - or not - magic show would you travel back to watch?
Any of the "old masters" - Thursen, Carter, Houdini, Chung Ling Soo. The problem with magic is that so much of what we do is lies and bluster and false memories of what really happened, it is very difficult to get accurate accounts of old magic acts.
We'd love to watch Houdini work a crowd, or see the Davenport brothers perform a spirit cabinet. Audiences' tastes change of course, so we probably would think it was all quite slow - Houdini once took three hours to do one of his escapes...
Who's the most disagreeable person you've come across in the industry?
A few months back a guy with a notebook came up to us after the show and told us that he was a magician, and that he really liked a couple of the tricks we had performed that evening. He then told us that he was putting on a show in a couple of weeks at the university he worked at, and he reckoned our tricks would go down well so he was going to use them.
When we seemed a little put out by the fact he had literally come to our show to steal our material, his response was simply "there are no new ideas". Luckily for the chap in question, there were other audience members around so we were having to be very polite, otherwise we'd have given him a couple of new ideas about where he could shove his notebook.
Is there a great trick you've invented that never seemed to work?
If a trick doesn't work with the audience then it is, by definition, not a great trick. But you do still miss the mark at times when you really think you're gonna hit.
We once wrote a trick about time travel that we thought was really clever - we got someone with a watch, synchronised it with a pocket watch on stage, then vanished it, and five minutes later it appeared on stage, now five minutes out of sync with the pocket watch, because it had travelled through time.
Actually, now that we write that down, there's no wonder it didn't land with an audience, it is FAR too complicated a plot to follow.
What's your best travel tip for gigging magicians?
Don't do it alone. If you do the work that we do it involves a LOT of travelling - we drive all over the country, and spend far more time travelling to and from gigs than we spend actually performing. Get a partner, it'll make the whole thing a lot more pleasant. 2am service station coffee is bad, but it's worse if you have to drink it alone.
The most memorable review, heckle or post gig reaction?
Our Christmas show ends with Mr West cutting a snowflake whilst reciting some fairly heavy-handed cheesy patter, all the while with Mr Morgan interrupting him.
We once had a child in the front row find this so funny that he ended up loudly exclaiming (at a reasonably quiet moment in the performance) "Stop it! Stop it you idiot!". We both lost it, as did the audience. His mother came to tell us afterwards that her son usually knows better than to call people idiots, of course.
How do you feel about where your career is at, right now?
Honestly? We're ecstatic. We do a couple of hundred shows a year in lovely theatres all over the country, performing to crowds of people who have specifically come to see us and the shows that we've written.
Our name on the ticket, our name above the door. When we first started out doing this job, this was the dream outcome for us, and after a lot of hard work we've got there. The slight problem is we didn't really know what a tiring dream it would be, so now we're working on recapturing some of that work/life balance we hear so much about.