Mulberry Bayswater "Cookie" bag

This is one piece that is a personal favorite and one I've wanted to showcase for the longest time.  The only reason I haven't is because I have not found any good pictures of Kate with this item.  Either the pictures are really bad or you can't really see the bag, as in the example below, which is the only picture I could find.

The bag is part of the Mulberry Bayswater collection, and from what I can find out it is a limited edition "Cookie" version, so called because of the cookie-cutter style scalloped edging.  The regular Bayswater collection is similar in style but plainer, without any scallop detail.  The picture below is the Cookie version that Kate is shown with, in beige pebbled leather.
The bag is quite rare and I found it impossible to find even an expired listing for this item!

Mulberry Bayswater "Cookie" via The Bag Lady.

Other Mulberry plain Bayswater listings that I've seen are priced at around $1,500 for the regular style bag, and about $1,300 for the smaller Bayswater satchel style.  They also come in a variety of textured  leathers, such as snake, ostrich, or smooth, which also affects the price.

The best repliKate I managed to find (other than outright "replicas" of course!) was this collection from ASOS.
First up is this leather satchel available in tan or black.  I'll admit that the style is not an exact match.   But you have to admit that it is a very good Mulberry-inspiration piece with the scallop detail in particular being on par with the original.  Another detail where it mimics the original is that it is actual leather.  And while the Bayswater has a postman turn lock style closure, this one has push lock closures reminiscent of the Mulberry push-lock style, so it is still very much in the Mulberry look.
This style is approximately $105.54 U.S., and as low as $84.43.  It comes in tan and black.

ASOS - leather scallop edge satchel in tan.

ASOS - leather scallop edge satchel in black.

Another ASOS style that seems inspired by this Mulberry look is the scallop edge satchel below.  It is boxier, hard framed, and synthetic leather.
This bag is approximately $38.70 U.S.

ASOS - scallop edge satchel.

Mulberry "Polly Push Lock" bag

The Duchess embarked on her and Will's North American tour a navy ensemble and accessorized with a Mulberry satchel bag (below left) in the style called "Polly Push Lock".  She's also been seen carrying the bag on other occasions, such as shopping (below right).

Below is a closer look at the bag.  Kate is carrying it with the back facing out but as you can see, the pebbled leather satchel is black, with brown strap accents.  The two strap options allow you can carry it by the handle like HRH or you can carry it cross-body style.  It also has an envelope style flap with push lock closure.
This bag appears to be no longer available but priced from ≈ $1050 U.S. as low as $588.

Mulberry via Net-a-Porter  - Polly Push Lock.

The notable details of this piece is the triangular envelope style flap, push lock clasp, and of course the dual straps with the handle attached at the top.

One two tone repli-Kate that I managed to find was this color blocked satchel style from Newport News.  Like the Mulberry, it has two toned accents, as well as dual straps with the handle attached at the top.  This style has a turn-lock clasp.
Retails for ≈ $149 U.S., as low as $99.

Newport News - colorblocked satchel bag.

I almost don't want to call this one below a "cheaper" alternative because its not very cheap -- yet considerably less than the original -- but its still a very nice looking bag in the Mulberry style and it is leather.

This all-black bag features the dual strap detail with the top attached handle.  Another notable feature is the push lock clasp, true to the original.  A slight difference is in the flap top, with is not an angled envelope style.

Retails for ≈$170 U.S.

Topshop - black leather push lock satchel.

In my search for this look-a-like of Kate Middleton's Mulberry bag I found that there are actually many variations to suit a variety of tastes.  It would be very easy to find a lovely bag to suit your own individual personality and needs, and even if it is not exactly similar to the original it will very much echo the basic style.
To aid your personal search you should note that this style of boxy bag with handle and cross body strap is referred to as a "satchel", but that description can also include a wide variety of other shapes and styles.