Catalysis of the reaction: 3-O-{alpha-D-GlcNAc-(n)-(1->4)-beta-D-GlcA-(1->3)-beta-D-Gal-(1->3)-beta-D-Gal-(1->4)-beta-D-Xyl}-L-seryl- + UDP-alpha-D-glucuronate = 3-O-{(n+1)-(1->4)-beta-D-GlcA-(1->3)-beta-D-Gal-(1->3)-beta-D-Gal-(1->4)-beta-D-Xyl}-L-seryl- + H+ + UDP.
N-acetylglucosaminylproteoglycan beta-1,4-glucuronyltransferase activity