Mysql regexp to allow numbers and '+'

First, use NOT REGEXP instead of !=1. To allow + at the start optionally, use ^\\+?. Since + is a special character in regular expressions, it must be escaped with a backslash (which must be escaped with another backslash). You then need one or more digits ([0-9]+), up to the end of the string $.

$query="UPDATE table SET phone='NULL' WHERE phone NOT REGEXP '^\+?[0-9]+$'";

This will match anything that doesn't begin optionally with +, followed by digits only. If you also need to permit hyphens and dots in the phone number, add them into the [] character class:

'^\\+?[0-9.-]+$'