How many possible img tags might be in your string? Assuming 1 then forget the global flag (and iterating through an exec) and simply make a regex that explains the whole string and use capture groups. Then you can specify, in your index of match, to return the capture group you know will represent it. Since, in these types of questions, there always seems to be a caveat not mentioned I made the expression more tight against some possibilities like other attributes in the element. So just in case it is more complex than you let on you can use this regex:
(?:<img )?[^>]+src=(["'])(.*)\1
The quote capture group is necessary so that you match up the quotes. You show double quotes but is that guaranteed? in this regexThe second capture group is always going to be the URL (contents of src to be more precise).
In code:
var str = '<img src="http://www.omgubuntu.co.uk/wp-content/uploads/2013/12/Multim.jpg" />';
var src = str.match(/(?:<img )?[^>]+src=(["'])(.*)\1/)[2]