No not really, but you're attempting to "do" London in a day and Paris or more likely Normandy in much less than a day, so maybe a better idea may be to get over your jetlag in the area that you are really interested which is obviously Italy.
Your day 1 will be on a jet, probably overnight, with you arriving in the morning of day 2. So Day 2 you will be a zombie (probably but some people say they are ok) and by the time you clear the airport and reach your hotel in London it will be pushing noon. Lunch, check in and getting to your first attraction by early or mid afternoon. You will be tempted to take a nap but you don't have time for that, and it is best for jetlag if you stay outside in the bright daylight. Early to bed.
Remember that it is likely that one or more of the 4 of you will suffer more than the others, yet the entire group will have to move at the speed of the slowest person or people.
Day 3 you may be able to see a few things from the outside. What things are top on your London list? If you plan to fly to Paris you will need to budget an hour to get to the airport (which one?) and 2 hours to check in, and at least an hour from the Paris airport to your hotel. So flying takes about 5 hours, plus you will lose an hour changing time zones to Central European Time.
Or you could take the Eurostar train which goes from centrally located St Pancras International in London to equally central Gare du Nord in Paris. You need a minimum 30 minutes (strictly enforced) check in time but an hour is what I currently advise. 15 minutes or so to get there, 2:20 on the train, 15 minutes to a hotel in Paris means that the train experience is much faster at around 3:50 instead of 5:00. Oh, except when you fly you also need to collect the check in luggage (which you have to pay for) and go through Immigration after you land which all add time, whereas with the Eurostar you go through both French and UK border control right after security, and since you carry all your luggage onto the train with you there are no waits to reclaim it.
Day 4 I will assume that when you say Normandy you are using shorthand for the WW2 US D-Day invasion area. The Normandy beaches and bocage area are huge and very poorly covered by public transport. You will probably need a guide. Most tours are a very full day but with trains taking over 2 hours each way you clearly won't be able to do that so you will be stuck with a half day tour which will give you a much smaller overview of the battles. Even with a half day tour you will arrive back in Paris very late.
Unless somebody is deeply in love with Paris or Normandy or London which are all getting just a lick and a promise perhaps giving over the whole trip to Italy would work better. Fly into Venice, fly out of Rome.
On the other hand if you want to properly see some of any of those you should take time from Italy so you can see enough of them so you don't look back and see yourselves as the Griswolds or the group in If It's Tuesday, This Must Be Belgium.