Good question. Our house is not brick, but was built in 1926. I debated about pulling the paneling off the inside, drilling holes and blowing into the wall cavities. Then I considered pulling off some strips of siding outside and blowing it in that way. But with no vapor or moisture barrier under the outside sheathing, I finally chickened out on blown in. I just went ahead and ripped off the siding from the base plate to nearly the top plate and put in bats and protected that with overlapping tar paper. It was easier - sorta, better mostly because of no external vapor barrier - than gutting the inside walls and re-sheet rocking. However - given a little more $$$ I would have done the wreck out myself, paid a wall crew and had a better inside finish to the house.
With brick, if there are no cracks and there is at least something between the brick and the wall cavity, blown in should work. Foam is an option, but the contractor better get a good reading on each wall cavity or you'll be replacing sheet rock anyway. However - Not sure how you'd expect anyone to get to the top of the outside walls to cut a hole in the plate without pulling the roof.
One other thing - there may not be any fireblocking in there, then again there may be who knows what in the walls. I tore off (so far - not done yet LOL) about 100 linear feet of siding and I found all kinds of weird building BS in the walls. Enough that blown in would have been a serious waste of time. And the 18' of outside wall along the kitchen was a fricken nightmare of boards, spacers, blocks, stubs, abandoned outlets and whatnot. Also, you can only get under your windows with a hole on the inside.
If the house is worth the effort, I'd strongly consider tearing out the wallboard, upgrading any electrical possible and adding in the insulation. Another option - A good brick mason could probably remove several of the outside bricks near the top of the wall to allow the blow in, then match the motar and replace.