To me your list of locations is too much for 2 weeks but might work for 3.
Here's how I would break things down in to days "needed":
- London: 5 nights minimum for 4 full days, more would not go amiss
- Paris: 5 nights minimum for 4 full days, also more is better because, well, Paris is always a good idea, lol.
- Venice: 3 or 4 nights - that only gives 2 or 3 full days
- Florence: 3 or 4 nights - also only 2 or 3 full days
- Rome: 4 nights, or 5 nights if you do Pompeii as a day trip.
- Pompeii: There are day tour companies from Rome that do this as a day trip. I've not been, no idea if they are any good but it's a possibility. The other possibility is to go to Naples or Sorrento for 2 nights and see Pompeii on the full day you have in the area.
- Transit days over and back: You'll have 1.5 days going over, so one night on the plane and one full day coming back.
Looking at what I would want for minimum days for seeing these locations that puts you at the end of 3 weeks at best.
I, too, would do as Valadelphia suggests and go North to South starting in London, Eurostar train to Paris, fly to Venice and work your way down.
Since Italy seems to be your interest you might want to look at Rick's Best of Italy in 17 days. That tour does not go to Pompeii but you could add a few extra days in Rome and do it then.
