I'd probably go to the UK last. If you enter Schengen through Italy or France, you're unlikely to have a real conversation with an agent, but the UKBA loves asking questions. If they find out about the criminal history, it's a toss-up about whether your friend gets in. If that's at the start of your trip, denial of entry into the UK could affect ability to enter other countries using SIS. Conversely, if it's at the end, at least you've been to 2/3.