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.