" Solved with pavucontrol. I had already tried the
pulseaudio volume control, but you need to do a particular thing to make
it work.

First, install pavucontrol:

sudo apt-get install pavucontrol

Then start it:

pavucontrol

You'll get the volume control window. Now, you could go to "Input
devices" and select the webcam microphone as your input source: THIS
WON'T WORK. This is how you do have to it:

• Click on the "Recording" tab. This tab shows the applications that
  are capturing audio in that very moment, so it will probably be empty.
• Start skype then call the Echo / Sound Test Service (or anyone you like who will answer)
• When the other party answers, Skype begins capturing audio and will
  be shown in the "Recording" tab of the pulseaudio volume control window
• From the "Input from" drop down list, select your webcam

And voilà, you'll get your microphone back.

Alternatively, as described in SkypeTroubleshooting

• [..] go into the Skype Options menu - Sound Devices
• remove the tick at: Allow Skype to automatically adjust my mixer levels.
• Click Apply.
• Readjust the sound mixer controls (pavucontrol input devices will work now).

This worked fine for me.