My spouse and I are taking a 10 day vacation to Italy in March. We're traveling with British Airways and stopping over for 7 hours in London. We arrive at Heathrow and then need to transfer to Gatwick for the rest of our leg to Italy. Do we need any type of visa to do this landside transfer? We are US citizens, and we are planning on taking the Tube to London Victoria from Heathrow, getting lunch somewhere nearby the station and then taking a train (Gatwick express) to Gatwick from Victoria.

Also, for the 10 day trip to Italy, do we need to apply for a visa there?

Thanks.