The pair's new track failed to reach the top spot in the charts and landed at number two after Cee Lo Green shot to number one with his single Forget You.
Shame is the first single the pair have worked on since Williams, 36, left Take That 15 years ago and he will be releasing his new single and album with the band next month.
Other acts in the top ten this week included Tinie Tempah, Bruno Mars, Kings Of Leon and Katy Perry.
Cee Lo is also known for being part of the musical group Gnarls Barkley along with pal Danger Mouse.