Your itinerary is trash mainly because you're going to see City.
jk.
I'm assuming you don't have kids. How old are you? I've done similar itineraries through those exact cities (minus Zurich) several times but only out of necessity (we have family in each of those places). It's hard man. If you're < 35 years old it's doable but honestly you won't get as much enjoyment out of it as if you'd take your time. I would suggest 14-16 in Manchester, take the train down to London on the afternoon of the 16th and then take the train to Paris on the 20th. Forget Zurich.
There's not that much to do in Manchester. A day trip from London to Oxford isn't crazy, I've done it several times. Takes a couple hours by car or train- if you leave in the morning you can get back at night for a late dinner after a full day in Oxford. But even if you don't leave London there is so much to do in London. Catch a show. Go to a museum. Go to a concert at St Martin in the Fields. Go see a historical site. Go shopping. Go to Brick Lane, or Chinatown, or even go gambling if you want.
See the sites in Paris (will you go back soon? If not spend a day at Versailles) but also don't do too much in one day. One or two sites each day and leave time to just stroll and sit down at a cafe to peoplewatch or get lost in a neighborhood or walk a park. There's a crispness in March in Paris where you can just sense the city start coming back to life from winter. I can't explain it but you can sense the energy.