Others have already explained most of the sensible ways of doing this, and FWIW I'd just use the circular saw in your case, but this is fairly trivial to do by hand, and the tools are very cheap.
Rip-cutting 3m of 25mm (1") board by hand isn't fun, but it isn't hard either. The most important thing is to get your body in the right place: shoulder in line with the cut, arm swinging 'like a snooker cue', i.e. the saw can move up-and-down, but runs exactly true side-to-side. This will require moving your feet unless you have the experience to know where to stand. Then the only hard thing about a normal rip cut is starting it off. Once you've got the saw running smooth and straight, you angle the front side down 30 degrees or so, and the saw blade effective forms a fence against the previous cut, more or less keeping you perfectly in line without having to try. Believe it or not this is actually easier in thicker stock for this reason.
Then you just have to keep going: standing on the bench/table can help, as can using both hands. Long strokes cut more than fast strokes.
This can be done with a £10 hardpoint saw, the kind you can buy in any DIY shop: the teeth aren't ideal for ripping, but they are designed to do it. (Of course it's easier with a proper rip-cut saw, but if you had one of those you wouldn't be asking...) 22tpi for hardwood, or 16 for pine (yes, even when ripping: it's a hardpoint saw).
Of course, for your case you'll need to cut out a section to start the cut off. This can be done purely with the saw, cutting diagonally into the corner, then away, to make an 'M' shaped cutout, before flattening the middle, although it's probably quicker to use a chisel to remove the waste as suggested above (I wouldn't like to do that over 3m of stock, although it's perfectly possible and if done carefully will work fine).
When all is done you need a plane to clean up the edge: any half-decent #4 is fine if it's sharp (and sharpening is much easier than you might believe).
Would I do this for this job? No way: that's what I've got a plunge saw for. Have I done it? Yes, and in 2" stock, too. You only make the cut once, but you get to keep the furniture :D