The external wall of my house is a double-thickness solid brick wall (i.e. about 210mm thick consisting of 100mm brick, 10mm mortar down the middle, then another 100mm brick). I need to cut a new opening in this wall. I've already removed some bricks to insert a lintel (or rather a pair of lintels, one on the inside and one on the outside), but removing the bricks by cutting the mortar out around them was very labour-intensive. Is there an easy way to cut through a wall of this thickness with a straight vertical cut without spending a fortune on tools?
The "traditional" way to do it is, as you have suggested, to cut the bricks out by hand (and refit the cut bricks once you've done to give a tidy edge). It can be a time consuming job.
The more usual way to do it once the lintels are in place would be to use a disc cutter - usually a petrol driven one - (aka a rotary cutter or Stihl saw, after the common brand) with a diamond-tipped blade to cut through the bricks. This will make a lot of dust. You can get a water pack to reduce the dust (and cool the disc, reducing the wear on it), but it can still make for a messy operation, as the water will make the dust into a slurry that the disc will spray about.
You can hire the saws from pretty much any plant hire outlet, who will also hire the diamond tipped blades, charging you per milimetre (or half milimetre) of wear. That can be expensive though, so if you've a lot to do, it might be cheaper to buy the diamond-tipped disc from an independant supplier.
I've also seen what is basically a chainsaw with a diamond tipped chain for cutting through walls, etc, but I've not actually seen one used to comment as to how effective they are.
Don't forget that you should use eye, ear, and dust protection if you're doing work like this.
If you dont want to spend the money to rent a larger saw. You can get a masonry blade for your circular saw. Drill a hole through each corner use these holes to make a straight line and make a cut from both sides. With a 7 1/4 blade it will not cut all the way through but it will cut enough that you should be able to bang it out the rest of the way with a sledge hammer with a fairly clean cut.