The tributes have been repeatedly attacked and removed from a fence opposite the home where he was stabbed.
Residents have described them as being "in poor taste".
The row has put a strain on police resources, according to Sir Craig.
The 37-year-old, along with Bill Jeeves is suspected of burgling Richard Osborn-Brooks' home on South Park Crescent - which remains cordoned off by police - on 4 April.
Since Mr Vincent's death the floral tributes had been appearing on the fence opposite Mr Osborn-Brooks' home.
In the middle of Monday night the flowers and balloons were taken down and placed on the pavement by an unknown man.
By Tuesday lunchtime the family of Mr Vincent - understood to be part of the travelling community - put them back up on the fence, however 30 minutes later a second man tore them down, put them in a pile and stamped on them.
The tributes were reattached for a third time at 17:00 BST, but at 21:30 BST another man turned up and took away half of the bouquets.