Using Autofac for DI into WCF service hosted in ASP.NET application

I'm having trouble injecting services dependencies into my WCF service using Autofac 1.4.5. I've read and followed the Autofac wiki page on WcfIntegration but my debugging shows me that my WCF service is created by the System.ServiceModel.Dispatcher.InstanceBehavior.GetInstance() method and not by the AutofacWebServiceHostFactory. What am I doing wrong?

I've set up my ajax.svc file to look like the one in the example for use with WebHttpBinding:

<%@ ServiceHost Language="C#" Debug="true"
    Service="Generic.Frontend.Web.Ajax, Generic.Frontend.Web"
    Factory="Autofac.Integration.Wcf.AutofacWebServiceHostFactory,
             Autofac.Integration.Wcf" %>

My WCF service class Ajax is defined like this:

namespace Generic.Frontend.Web
{
    [ServiceContract]
    [AspNetCompatibilityRequirements(
        RequirementsMode = AspNetCompatibilityRequirementsMode.Allowed)]
    public class Ajax
    {
        public MapWebService MapWebService { get; set;}

        public Ajax() {
            // this constructor is being called
        }

        public Ajax(MapWebService mapWebService)
        {
            // this constructor should be called
            MapWebService = mapWebService;
        }

        [WebGet(ResponseFormat = WebMessageFormat.Json)]
        [OperationContract(Name = "mapchange")]
        public MapChangeResult ProcessMapChange(string args)
        {
            // use the injected service here
            var result = MapWebService.ProcessMapChange(args);
            return result;
        }
    }
}

Now I've used the wiring up in the Global.asax.cs as shown in the wiki mentioned above:

var builder = new ContainerBuilder();
builder.RegisterModule(new AutofacModuleWebservice());
var container = builder.Build();
AutofacServiceHostFactory.Container = container;

with

class AutofacModuleWebservice : Module
{
    protected override void Load(ContainerBuilder builder)
    {
        builder.Register<Ajax>();
        builder.Register<MapWebService>().ContainerScoped();
    }
}

In my web.config I have

<services>
    <service name="Generic.Frontend.Web.Ajax">
        <endpoint address="http://mysite.com/ajax.svc/" binding="webHttpBinding"
                  contract="Generic.Frontend.Web.Ajax" />
    </service>
</services>

.

The service already works fine but I can't get the Autofac bits (read: creation/injection) to work. Any ideas?

Edit: Removing the default constructor unfortunately leads to the following exception:

System.InvalidOperationException:
The service type provided could not be loaded as a service because it does not
have a default (parameter-less) constructor. To fix the problem, add a default
constructor to the type, or pass an instance of the type to the host.

Cheers, Oliver