It's a strange looking stucture that.
This looks like a job where the use of power tools that a tradesman has access to would shorten the time and take the 'grunt' out of the job. In particular, a brick saw to cut vertical lines in the new position for the steps, and through the concrete above it to form the new edge where the steps would descend. Bricklaying itself is not easy first time around - getting the gist of using a string line to keep the rows level and the right amount of mortar layed.
I would urge you to consider speaking to a contractor - one that might be happy for you to do some the labouring perhaps.
The project steps would appear to be:
Cut the vertical brick lines, and a U-shaped slots in the concrete above to free the existing structure from the material to be removed.
Fill in the front of the old steps with bricks - tying into the existing - with brick toothing or some other method (depends how neat you want the finished job).
Dig out the new steps area - moving the material directly to fill the old 'hole'.
Construct some shuttering at the side of the new hole and backfill with concrete. Fill the top of the old hole with concrete at the same time.
Construct the new steps in either brick, concrete or paying slabs.
Here are some general guidelines from Bexley council (building control) about issues with garden walls. These don't formally apply to you. Note that they recommend (and I'd agree) that a wall this height should really be one brick thick - your's appears to be a half-brick thick. It's probably not an issue as yours probably has some concrete infill behind the front-face. You won't know until you try and pull it apart.
http://www.bexley.gov.uk/service/planning/buil dingcontrol/hg11.html