U.S. citizens need only a valid passport to enter Great Britain for stays of up to six months. Travelers should be prepared to show sufficient funds to support and accommodate themselves while in Britain (credit cards will usually suffice for this) and to show a return or onward ticket. If you're within six months of your passport's expiration date, renew it before you leave—nearly extinct passports are not strictly banned, but they make immigration officials anxious, and may cause you problems. Health certificates are not required for travel in Scotland.
If only one parent is traveling with a child under 17 and his or her last name differs from the child's, then he or she will need a signed and notarized letter from the parent with the same last name as the child authorizing permission to travel. Airlines, ferries, and trains have different policies for children traveling alone, so if your child must travel alone, make sure to check with the carrier prior to purchasing your child's ticket.
U.S. Department of State (877/487–2778. www.travel.state.gov/passport.)