Can't get ScrollViewer to work within ItemsControl>WrapPanel

I have the following code:

<ItemsControl
  ItemsSource="{Binding ItemsList}"
  Visibility="{Binding HmiState, Converter={StaticResource IsHmiViewState}}">
  <ItemsControl.ItemsContainerStyle>
    <Style>
      <Setter Property="FrameworkElement.Margin" Value="5" />
    </Style>
  </ItemsControl.ItemsContainerStyle>
  <ItemsControl.ItemsPanel>
    <ItemsPanelTemplate>
      <WrapPanel Width=300 Height=200 ItemsHost="True"
           ScrollViewer.CanContentScroll="True"
           ScrollViewer.VerticalScrollVisibility="Auto" />
    </ItemsPanelTemplate>
  </ItemsControl.ItemsPanel>
</ItemsControl>

It display everything up to the 200 height correctly (wrapped), but doesn't display anything below that and there's no scroll bar.
ItemsList is an ObservableCollection.

Does anyone have any suggestions?

There should be a ScrollViewer that hosts an ItemsPresenter in the ControlTemplate of the ItemsControl:

<ItemsControl ItemsSource="{Binding ItemsList}" Width="300" Height="200">
    <ItemsControl.Template>
        <ControlTemplate TargetType="ItemsControl">
            <ScrollViewer>
                <ItemsPresenter/>
            </ScrollViewer>
        </ControlTemplate>
    </ItemsControl.Template>
    <ItemsControl.ItemsPanel>
        <ItemsPanelTemplate>
            <WrapPanel/>
        </ItemsPanelTemplate>
    </ItemsControl.ItemsPanel>
    <ItemsControl.ItemContainerStyle>
        <Style TargetType="ContentPresenter">
            <Setter Property="Margin" Value="5" />
        </Style>
    </ItemsControl.ItemContainerStyle>
</ItemsControl>