You may wish to review the prior article about function of the pressure relief valve.

The quick attention grabber here is the number 3 plug in bore C. This drilling is used to pass oil from the oil pump to the input end of the pressure relief valve, and it needs to be plugged at the bottom. If this port is left open it will allow oil from the pump to return directly to the sump, and there will be no oil pressure.
I see occasional messages noting this problem after a professional engine shop worked on the engine. The oil gallery plugs are commonly removed before hot tanking so the drill holes can be checked and cleaned out with rifle brushes. After machining of the block and a final pass at cleaning, the oil gallery plugs are replaced. Even a pro shop may occasionally make a mistake and plug the wrong hole. If port C has no plug in it, you need to install one.

Another thing that can cause no oil pressure in an Austin B-series engine is use of the wrong gasket for the oil pump. Picture below left shows gaskets for the three main bearing engine (1953-1964) at top and for the five main bearing engine (1965-1980) at bottom. Center picture shows the incorrect 3-main gasket being installed on the 5-main engine. Picture at right shows the 5-main oil pump. Problem is that the later oil pump has an extension of the intake port exposed on top of the pump body, but that port is not used on these engines and must be sealed. Installing the smaller gasket for the 3-main engine leaves this port exposed where air can be drawn into the pump, and it will not pump oil.