My property is the only one I can see on this estate without a stench pipe. It is a detached one-bedroomed bungalow and I am of the understanding that the drainage system is somehow connected to my next door neighbour (if that makes any difference). Out of interest, is this normal and/or legal? Everything at the property seems to work all right.

A great deal depends on where you live and how old the house is. It would not be up to international building code now but maybe back in the day. How close is the neighbor and is this city sewer or septic. Basically all drains need traps and vents. It is also possible that you have AAVs in the home. A mechanical Air Admittance Valve could be under your sinks, look around after the P trapo for a short verticle pipe and a funny looking cap. Got one?

Can't see one. The house was built in around 1960 (or in 1960). My lateral connects to the main sewer.

What town/state/country. 1960 is a bit too new to get the back in the day labe.