Through the centre of the joist sounds like an option.Unless its really old fat/thick 16" pitch pine joists then nope - do not notch for a 40mm pipe. Anything above a 200mm joist though can be drilled though and get the waste through the centre of the joist.
The joist needs to be at least 400mm to take a 50mm notch which would be the min to take a 40mm waste pipe. If you have a basin and a shower on the same run then the waste would ideally increase to 50mm at the tee or be on their own run depending on distance. Having anything else on a shower waste run only temps, when restricted, for the waste to end up in the shower tray so at least a 50mm pipe will help with that.
Distance from shower tray to soil stack is about 2m with about 1.5m to the basin (on the horizontal). I might have to remove a bit of the current boxed in section to have a look at what is used currently.
8x3 joist is massive, are we talking mid span or against the wall, are they underspanned, how many need notching? No-where near enough information.
The joists are the traditional solid timber - I remember seeing them when I was pulling alarm cables but I am taking a bit of a guess on dimensions. I can check the 8" dimension from the landing.He said house 2000 - no one has mentioned the possibility of the joists being engineered I joists - would be an even bigger problem
The en-suite is between the structural walls (Block) of the kitchen / utility room and lounge on the ground floor. One wall is just under the soil stack next to the toilet. The other structural wall is about 600mm the other side of the wall with the basin on.
The stairwell is to the left of the en-suite and I would assume that the joists run top to bottom per those on the landing

