I'm looking to move and upgrade my speakers (see photo). Positioning isn't ideal but it should be better than my current set up. Considering PMC Prodigy 1s as they're front ported and fairly unfussy about positioning. But the shop has also suggested B&W 707 S3s, which are rear ported. The speakers will sit about 20cm from the rear wall, will there be much difference?
Haven't read the thread, only skimmed it.
The B&W sounds like a typical dealer recommendation - steer clear - they're just trying to sell you what they want to sell you, with zero consideration for your room.
It looks as though you have a fairly live sounding room, so avoid bright sounding speakers, especially those that just have the tweeter string on the front face of the cabinet, as you'll have treble bounding off your side walls, floor, and ceiling. Look at speakers using waveguides, which will minimises the HF dispersion and reduce reflections, reducing any potential brightness caused by the room.
In your chosen position, not only will you get HF reflection off the side walls, but also more HF reflection potentially off the inside of the chimney breast, which will also end up being deflected to the outside walls, exaggerating it further, and maybe creating a bit of time smear.
Putting loudspeakers in bookshelves is very hard to get right. Most speakers will produce too much bass to work in that sort of position, even if they are front ported, as enclosing a speaker within what is essentially another cabinet can add its own resonances. Two speakers that are more likely than most to work in that position are the Ophidian Minimo 2, which uses a rear vent (not port), and the Amphion Argon 0, which are rear ported, but has a more subdued bass due to their size. The latter are 26cm tall, but could be used on their side due to their low crossover point, so you could get the tweeters further away from the chimney breast to reduce any potential reflections, which will naturally be reduced by the waveguide anyway.
As well as finding a speaker that will work in that position, you'll need to find one that your amplifier can drive easily - if the amp struggles, you'll end up with a mediocre sound. Most speakers likely to fit into that space won't be very big, and therefore won't usually be too efficient. Sealed boxes will usually be even less efficient, and generally don't sound too exciting at lower volumes.
Ideally, you'll need to take into account some sort of isolation to reduce resonances travelling through the shelves and adding to the end result.