well, if you can see the incoming water service pipe, and it doesn't seem to be leaking (even in the garden outside) then you probably have the very common broken brown-glazed clay gulley.
Can you take some more photos into it.
Commonly, an old one will have had new concrete built up round it, because the leak washes away the soil beneath, and the original concrete cracks and sags into the void. The gully itself may have tilted and sunk. Any ground around it will be surprisingly wet and muddy, and the concrete may sound hollow when banged (due to the void below). The new concrete often bridges the dpc. See if you can find one.
If it is just rainwater you won't have wild tomato plants and red worms, but you may have slugs. nearby trees and bushes may be unusually lush, green and fast-growing.
If your house is close to the road you might not have a manhole, or it might have been buried or paved over.
If you put a gloved hand into the gulley you might feel a crack, but it may well be on the other side of the bend. The water level in the trap may be lower than it should.
As all the drains in your road are likely to be the same age, other similar houses may already have had theirs done. Look for a modern plastic downpipe and gulley, and concrete or paving that looks new, and may be at a different height to yours. Perhaps you can engage neighbours in conversation.
BTW, even if the leak is not from the waterpipe, ask your water company to test the drinking water for lead content. There might be a subsidy, or free reconnection, when the time comes that you replace the lead pipe with a larger plastic one. It may be a good time when you are digging up the drain.
Have you got a water meter or a person with sharp hearing?
Cameras are usually poked up the drain from a manhole, but I expect they could wangle one down the gulley. You may have an (iron) manhole in the road, but prod round your garden. if you look in neighbours gardens you may see where it is usually put.
Don't allow anybody who sells silicone injections near your house.