Consider that the fabric is made of orthogonally oriented fibers. The sofa is reportedly fire-resistant, so the burning rate is likely to be greatly retarded. The substrate structure provides the anisotropy in properties, and the material may burn better either parallel to the fibers or in 45-degree angle, which would explain self-organization into square shape.
A point-source ignition can be achieved with a sufficiently bright sun and a luckily positioned glass charm. Or a laser pointer. These things are fun.
Yeah but its in London in winter. I wondered about a burning cigarette left on or under the sofa hours earlier.
Was it anywhere near this building?
I think the shopkeeper doesn’t really understand laser pointers.
Who knew Delorean made pillows?
“Where we’re going, Marty, we won’t need sofas!”
Where is Charles Fort when you need him?
The fire hasn’t burned along the grain in either direction, it has almost burned exactly along the bias, but equally in both directions? I don’t think fabric grain can account for the shape.
Seeing the Christmas ornaments in the window (and seeing from the photo that it’s a relatively sunny day) my vote is for an ornament or bauble that forms a concave mirror. Sort of like the Fenchurch building melting cars in miniature. Then with a pre formed square shape we get equal expansion in all directions.
This is why I don’t use glass paperweights!
Uh, kinda easy to explain…
There was a cardboard box that had the bottom exposed to chemicals that would react (slowly) with the synthetic fibers of the couch. Said cardboard box got set on the couch for a few minutes and then moved elsewhere. Over time, the compound soaked in / heated up as it reacted with the couch. The couch is fire-resistant so the fire couldn’t spread beyond the contact point, where the slow chemical burn was occurring.
Result? Perfect burn pattern in the shape of the bottom of the box.
What chemicals?
Probably cleaning chemicals of some sort, but there’s a lot of options. Basically, it just has to be something that wouldn’t react with cardboard, but would react with whatever fabric (or possibly stuffing) the couch is made of.
Notice also in the picture that the square isn’t perfect - it actually is missing a corner where it goes over the side, but nothing down on that side is burnt - that offers a little more evidence it’s caused by contact with something instead of a spill or similar.
Maybe the square non-fire-retardant ‘fire-retardant-fabric’ label stuck on the fire-retardant fabric caught fire.
Undoubtedly Mooninites 
Ah, so you are implying that it was a terrorist act.
I had nothing to do with this fire.
Like what?
Oh, I didn’t realize you were a Boston cop. I didn’t mean to alarm you 
No need to worry, clearly this is just evidence that Bill and Ted have recently been there!
Anti mould chemicals. Regularly used.
