Where does the water from my kitchen go?

Twopints

I live in a bungalow which has the kitchen at the front and the bathroom and a utility room at the back.

Waste water from the utility room and bathroom runs along the rear of the house from left to right, then along the side of the house to the front, then from the side it runs from right to left to the middle of the house. This is where the kitchen is. If i flush the toilet or use the bathroom or utility room, I can see the water take this course through various drain covers, including one at the front of the house.

If I run the kitchen taps, nothing come through this drain. Where is it going?

There are no other drain covers, except for one small (6in x 6in) inspection cover, immediately outside the kitchen. This appears to be full of kitchen-type waste that would have gone down the sink, but again, when running the taps there is virtually no water coming into here, just a trickle.

The sink is not blocked but is sometime slow to drain, which is why I was trying to clear the drains.

Help, where's it all going??