you can call it from inside your code;
BrowseLineItems(p_web)
now depending one the exact circumstances, you may need to add one or more of the following lines;
p_web.DeleteValue('_EIPClm')
p_web.DeleteValue('_Clicked')
p_web.DeleteValue('_EIPRow_')
p_web.DeleteValue('_CallPopups')
most notably, where those values might exist before the call.
Because you are altering values, you also probably want to do this pretty "late", after all the other processing has been done, especially for Ajax calls. And I'm guessing it's only really ajax calls that you need to do this on (page calls would presumably just update the cart in the normal way.)
Cheers
Bruce