Its not a new barrel you need. I think we have ,as standard, a split spindle so the handle only works from the inside so,as "underhand"s friend has done, if you change the spindles then the handle will work from the outside.
Alternatively get a new spindle that will go through from one handle to the other then both handles will work
A thing to be careful of is the spindle size as what may seem the correct size might be a fraction bigger/smaller.
Don