Amazingly enough The Beatles did not have their first three songs reach number one.

Frankie goes to Hollywood had "Relax", "Two Tribes" and "The Power of Love," becoming only the second act in the history of the UK charts to reach number one with their first three singles.

The first group to achieve this fete was Gerry & the Pacemakers with their first three single releases: "How Do You Do It?", "I Like It" and "You'll Never Walk Alone".

This record remained unbeaten until the Spice Girls not only had their first three released songs reach number one but went on to achieve a six-single streak in 1996-1997. The six consecutive songs that reached number one were: "Wannabe", "Say You'll Be There", "2 Become 1", "Mama"/"Who Do You Think You Are", "Spice Up Your Life" and "Too Much".

More Info: en.wikipedia.org