Italy trip with London or no?

Venice and Florence need at least 3 nights each, if not more, and London needs much, much more. You really wouldn't even have two days there what with all the flying and getting to and from airports - I'd say save London for another time.

Keep what you have as each place deserves their due, and make yourself a promise that you will be back-to London. Have fun!!

In a word, no.

If you dropped Positano and took a night off Rome, allowing 3 nights in London, then perhaps.

no

I would echo the same: three nights gives you only 2 full days in each of these cities, and I think they deserve that if not more. Also, depending on the time of your flight home from Naples, it's possible you will need to spend 1 night in Naples itself. From a public transport perspective, Positano is not the best place to be located the night before an international flight if that flight is early to mid-morning...although if price is not a factor, private car service is a possibility.

London is a great city but it's very large, spread out, and really requires more than 1.5 days ( you'd possibly have even less) to take in the "main" sights. Some of those are also time-consuming, depending on your interest in history.

Also consider that at some points in this itinerary you'll encounter days that big attractions are closed. The less wiggle room you have to work around those, the more hectic the schedule. It's wise whenever possible to have a cushion against closings, unforseen transport delays, etc! :O)

Another vote for "no." A lot of travelling for what will amount to less than 2 days in London. London is a destination in itself.

No, absolutely not, unless you are one who would rather say you've been somewhere than actually seen somewhere.

There is one night missing in this picture. The night in Naples before your flight back, high is likely very early in the morning and therefor not convenient from Positano, which is quite a distance away.
An alternative is to fly back from Rome, in which case you would switch the sequence of locations in your itinerary and do Positano after Florence with Rome for last. It might seem a bit backtracking, but you save a night that way.

As suggested above, the only way you can fit London in your number of nights is with the elimination of Positano and the elimination of a night in Rome. In that case it would be advisable that you fly British Airways or their partner American Airlines (I think DFW has a non stop). Basically you would prolong your layover to a few nights rather than just a few hours.

I agree with other posters it seems too tight to add London. However, if you still want to squeeze it in, Consider going to London first. Looking at airfares I have found time and again flying back to the states from London is a killer in taxes.