"Sing", a souvenir collection including the Military Wives, Jamaican guitarist Ernest Ranglin, the Sydney Symphony Orchestra and Prince Harry playing tambourine, saw off other new entries from quirky UK singer Paloma Faith, Rumer and U.S. glam band Scissor Sisters.
The top five albums were all new entries in this week`s chart, according to the Official Charts Company.
Barlow`s success caps a momentous weekend of jubilee pomp and national festivities which have seen millions pour out into London`s streets to celebrate Elizabeth`s 60th year on the throne.
Rudimental featuring John Newman`s "Feel The Love" entered the singles charts at number one, the Official Charts Company said, dislodging We Are Young by Fun featuring Janelle Monae.
(Reporting by Matt Falloon, editing by Paul Casciato)