C# Generics – Initializing Generic Type with Constructor Parameters

I am trying to create a generic class which new's up an instance of the generic type. As follows:

public class HomepageCarousel<T> : List<T>
    where T: IHomepageCarouselItem, new()
{
    private List<T> GetInitialCarouselData()
    {
        List<T> carouselItems = new List<T>();

        if (jewellerHomepages != null)
        {
            foreach (PageData pageData in jewellerHomepages)
            {
               T item = new T(pageData); // this line wont compile
               carouselItems.Add(item);
            }
        }
        return carouselItems;
    }
}

But I get the following error:

cannot provide arguments when creating an instance of a variable
type

I found the following related question which is very close to what I need:
Passing arguments to C# generic new() of templated type

However, I can't used Jared's suggested answer as I am
calling the method within the Generic class, not outside of
it, so I can't specify the concrete class.

Is there a way around this?

I have tried the following based on the other question, but
it doesn't work as I don't know the concrete type of T to
specify. As it is called from inside the generic class, not
outside:

public class HomepageCarousel<T> : List<T>
    where T: IHomepageCarouselItem, new()
{

    private List<T> LoadCarouselItems()
    {
        if (IsCarouselConfigued)
        {
            return GetConfiguredCarouselData();
        }

        // ****** I don't know the concrete class for the following line,
        //        so how can it be instansiated correctly?

        return GetInitialCarouselData(l => new T(l));
    }

    private List<T> GetInitialCarouselData(Func<PageData, T> del)
    {
        List<T> carouselItems = new List<T>();

        if (jewellerHomepages != null)
        {
            foreach (PageData pageData in jewellerHomepages)
            {
                T item = del(pageData);
                carouselItems.Add(item);
            }
        }
        return carouselItems;
    }
}

********EDIT : ADDED POSSIBLE SOLUTIONS**

So I have tested 2 possible solutions:

First is exactly as explained below by Jon Skeet. This
definitely works but means having an obscure lambda in the
constructor. I am not very comfortable with this as it means
users need to know the correct lambda that is expected.
After all, they could pass a lambda which doesn't new up the
type, but does something entirely unexpected

Secondly, I went down the Factory method route;
I added a Create method to the common interface:

IJewellerHomepageCarouselItem Create(PageData pageData);

Then provided an implementation in each Concrete class:

public IJewellerHomepageCarouselItem Create(PageData pageData)
{
     return new JewellerHomepageCarouselItem(pageData, null);
}

And used a two step initialisation syntax:

T carouselItem = new T();
T homepageMgmtCarouselItem = (T) carouselItem.Create(jewellerPage);

Would love to hear some feedback on the merit of each of these approaches.