Using/Modifying WireShark to log http traffic

Wireshark can do that, simply by capturing the network traffic which would include HTTP traffic. You might want to use capture filters to limit the capture to http traffic only, for example using "tcp port http" and writing the files to disk using multiple files. You can do that by opening the capture options dialog. Reading the recorded trace might be a bit more complex than reading a "normal" log file, but you can export all packets to text files if you want to, or even reconstruct http content.