OK. Any or all of those are likely to be leaking, because the clay pipe in the ground usually snaps at the bend or the elbow. There might be an old house somewhere in the country that does not have broken and leaking gullies or drains, but I have never seen it.
Clues:
Where the mortar between the bricks has been washed away, or, as by your kitchen has been washed away and refilled.
Where the surrounding concrete surface has sunk and cracked, or moved away from the house wall, or been filled in
Where there is a damp patch around the pipe or drain
You can get a CCTV survey if you want, where they poke a camera up the drain and have a look.
You will get water from a broken drain, and it will be worse if the drain is blocked further downstream. Tree roots like to grow into broken drains.
Digging out and relaying drains is a simple job, but a bit wearisome as it involves gigging holes and trenches. It's a job for a builder or groundworker rather than a plumber (plumbers are weedy little fellows with petal-soft hands) but some advertise themselves as sanitary engineers and can use a shovel. A sturdy DIY woman who can dig trenches and follow instructions can do it. I think you will have to notify your local Building Control officer who will inspect the new drains before you cover them up.
My advise is not to waste your money on "damp-proofing" treatments.
Try and get a personal recommendation for a local small builder who's been in business for some years and not gone bust. As well as the drains, they can repair the brickwork where it has been loosened or eroded below ground.
Assuming that the cost of relaying the drains will be some thousands and you can't do it straight away, I would get a survey done and a report.
I don't believe it's worth trying to do piecemeal repairs. When you dig up a bit of clay pipe, you usually find the one it joins onto is also broken. When you dig out that one, you find....
I wouldn't be at all surprised if they've been broken and leaking, and slowly getting worse, for about 77 years.
If you want to sensibility check my opinion, dig a small pit next to the bathroom drain, and look in it immediately after you've had a bath and pulled the plug. I've stood in a hole and had it fill up with bathwater before now.