Just a couple days ago I purchased a 2005 mcs. This morning I cranked it over and noticed a "chirping" noise coming from under the rear seats. It only happens on cold starts. There is also a smell of fuel that fills the car. As far as I can tell there hasn't, for the 2 days I've owned the car, been a drop in power.

I did have a Mini dealership inspect the car before I purchased it, and they had told me nothing was wrong. They did not have a chance to cold start the car, so it may have been missed. When I bought the car I was given a 3 month 3,000mi warranty on the drivetrain.

Am I right to think that it is the fuel pump causing this?

 

The pump can be heard when you put key on position 2 right before cranking. That means it's priming & that's normal. If you wanna check further, you may use a fuel pressure gauge attached to the fuel injector rail Schrader valve under the intercooler. You should read around 52psi prior to start up, around 40+psi on idle.
Fuel stench in cabin? You shouldn't have that. Pull out your rear seat & observe upon start ups. The pump is on the LH side, filter on RH. Both are seated on identical rubber seals. Check for leaks around both assemblies.

 

the chirping is the evap canister.