My factory fitted Electric Fuel Pump was working but was leaking out centre of it. I removed it, fitted a spare now have I no power at the 2 fuel pump electrical connections.
The replacement pump works if I connect it straight to the battery but is showing no power at the 2 fuel pump electrical connections.
Any pointers?

First thing I'd d is put test light/multi meter on the two wires, between them, see What you have. Check power to supply wire using car body as earth for test light, if it has it could be bad earth.
You don't mention what car it is so i'm assuming early model? If so, check bad connections/ broken wire/fuses etc. If you let us know the model, me or someone else may be able to help.

What year model are we talking about anyway?

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SooperDooperMiniCooperExpertEngineering

All garage work involves equal measures of enthusiasm, ingenuity and a fair degree of irresponsibility.