If you are using MVC then you can inherit the EPiServer AuthorizeContentAttribute, implement IAuthorizationFilter and inherit a custom OnAuthorisation method that you can then use to redirect to your login page. This attribute needs to be applied to each page controller where you want this rule to be applied. A very quick/simple POC can seen below that does this:

public class CustomAuthorizeContentAttribute : AuthorizeContentAttribute, IAuthorizationFilter
{
    public void OnAuthorization(AuthorizationContext filterContext)
    {
        base.OnAuthorization(filterContext);
        //Check if user doesn't have authorisation to the content
        if (filterContext != null && filterContext.Result != null && filterContext.Result.GetType() == typeof(HttpUnauthorizedResult))
        {
            // Check if the user is logged in
            var context = filterContext.HttpContext;
            if (context.User != null && context.User.Identity != null && context.User.Identity.IsAuthenticated)
            {
                //User is authenticated and they don't have access so redirect to not authorised page
                filterContext.Result = new RedirectResult("/not-authorised-page/");
            }
        }
    }
}

Example controller (from AlloyMVC):

[TemplateDescriptor(Inherited = true)]
[CustomAuthorizeContentAttribute]
public class DefaultPageController : PageControllerBase
{
    //Code
}

If you are using WebForms you can override AccessDenied on PageBase: http://world.episerver.com/Documentation/Class-library/?documentId=cms/7.5/EC4A185.

Let me know how you get on.

Thanks!  I am using MVC, and ended up finding Tarjei Olsen's post which outlined overriding a controller's OnAuthorize once I changed my search query to Access Denied, but your solution looks even a little simpler.  Thanks a ton!