There are actually seven music boxes in Westminster, but they've been split between Buckingham and the rest of the borough. Here are the first four.
Secret #31 - Westminster
The music box is right next to Victoria Station.
From the viewpoint at Victoria Station, look down to the left. The Secret is in the garden of the houses below.
Drop down to the tracks below and drop off the side.
Hop over the wall to the right to access the garden - the railings are too spiky to jump over.
The music box is on a table.
Secret #32 - Westminster
The next Secret is to the south of Belgrave Square.
Get yourself to the south end of Belgrave square.
With your back to the park, climb up to the roof of the house on the corner.
The music box is up here.
Secret #13 - Westminster
The Secret is in the park to the south of the Houses of Parliament.
You can access the park from the street.
The music box is on a bench to the right of the statue.
Secret #28 - Westminster
The last Secret in this part of the borough is north of the Big Ben viewpoint, on the roof of Richmond Terrace.
Make your way to Richmond Terrace (opposite The Foreign Office) and climb up to the lower balcony.
The music box is up here. It will be where Evie is perched in the screenshot above.