Why is my '01 Toyota Hiace hard to start on a cold morning?

My 2001 Toyota Touring Hiace (Regius) with the 2.7-litre petrol engine is very difficult to start on cold wet mornings. I really have to work the accelerator, she tries to fire up, but just splutters. If I do get her to run, I have to sit and warm the engine for 3 or 4 minutes, because she has no pulling power! Once started, she starts well for the rest of the day. I have changed the plugs, cleaned the carburettor, and airflow sensor. A garage has suggested the fuel pump is not providing enough pressure. Could this be the problem, or is there anything else for me to try?