How can I build and install kitchen cabinets?
I have built many islands using top cabinets - they don't have bases.  The easiest way to add a base is with some 2x4s (or 2x6s for height).  You will just build a simple rectangle with bracing for each cabinet.  I guess you could build a big rectangle for a row of cabinets but I have been down that road and it won't be traveled again.

Basically you just need to decide how you want this to look.  Do you want a ledge (common in america) or do you want it flat?  Ahh and then the last thing.  You will need to put on a face plate on this section that matches the rest of your cabinets.  If you are going to have a 4 inch ledge... no big deal just make sure all of your rectangles project at the same depth.  But if you want it flat then you really have to be precise and take account for the depth of your face plate.  

About Brick.  I wouldn't even think about it.  Brick gets its strength from being surrounded by other brick - kind of like tiles.  I don't see it being strong enough on its own to handle the weight, movement, or whatever unless you build a solid brick brick.  Also you are going to deal with a ton of other issues like how do you secure the brick to cabinet and how do you keep the bricks even across all cabinets...  Can brick be done?  For sure.  But expect a ton of time and it will need a few rows for sure - and I am not sure what you plans are if it isn't close to level.

Another alternative is get some screw in cabinet legs... we buy them at IKEA here.