London to Rome

No, quite simply. It is a two hour flight to Rome, not factoring in the return flight and getting to and from airports. I assume you live in New York - as a point of comparison, do you think you could do a daytrip to Minneapolis?

If you've booked to go the UK then stick with that. If you want to see more of the country take daytrips to places like Bath, or maybe spend a few nights in Edinburgh, which are accessible by train. You could even take the Eurostar to Paris and spend a few nights there before returning. If you insist on going to Rome, spend two or three nights there so you can properly experience the city. It will stress you out a lot less.

I can't imagine doing Rome as a day trip from London. There are so many great things to see in the UK I would just stick with that and save Rome for its own trip as there are so many great things to see there as well.

I live in Rome and cannot fathom doing the reverse. We flew to London a few months ago and the door-to-door time using public trans in Rome and a combo of local train and taxi in London was almost 8 hours. You might shave an hour off of that if you went cabs all the way, but there is no avoiding security lines, waiting times, and delays. Stay in fabulous London and spend 10 days in Italy another time.

I would stay in the UK and enjoy it. Rick has a 7 day tour that is entirely in London. If you want to venture outside of London, places like Bath, Stonehenge, Windsor, Canterbury, Winchester, Salisbury etc. come to mind. It is going to depend in what part of London you are staying. I could very easily spend 10 days in London, even after several trips.

No, not possible.

You could possibly fly in, tag one place, and run back to the airport. Unlikely you would have enough time to actually go into anywhere.

If you do want to do this, you can certainly do it as an overnight. Given the cost and hassle, I would only do this if you are sure you will never get to Rome on another trip and if seeing the Vatican and Colosseum are very high on your bucket list. However, if these conditions apply, go for it. The Minneapolis example given above is apt; from New York, if you really had something you wanted to see in Minneapolis (say a special art exhibit), you could definitely go for an overnight to see it.

To find airfares, use Skyscanner: http://www.skyscanner.com/. Be aware that, as far as the airlines are concerned, London has 6 airports and Rome has 2 airports. While both of Rome's airports will work, some of London's are much farther from the center than others, and will take more time and/or money to reach. On a short trip like yours, it's worth paying to use the closer in ones (London City is the closest, followed by Heathrow).

For any flight but particularly if you're looking at a budget carrier like Easyjet or Ryanair, be sure to go to their websites to do a dummy booking (up to the point where you put in your credit card). This will allow you to see all the extra charges, and to learn about all the rules and restrictions. Budget airlines make money from people who don't read the rules, or think that the rules won't apply to them. For example, if they say you can only have one carryon bag and that they charge for any checked bags, they WILL make you check any additional bags - at a higher fee than if you had booked a checked bag online before you got to the airport. Because of the additional fees on budget airlines, the "legacy" carriers like British Air and Alitalia can actually work out to be a better deal, and they are more likely to use the closer-in airports. Again, look at all the costs and hassles before deciding.

If this is a business trip then I would look at shaving 2 or 3 nights off the end for a visit to Rome, and fly home from there.