Ford focus 1.8 zetec - e manual 102k 2000

if i leave my car overnight and its been a cold night/morning it doesnt like to start proper

the engine cranks over wants to start but dies
second attempt same but the cranking is longer(5secs)and will start but only just a low idle 1000rpm

however if i was to accelerate it will fire up first time always
i know you should never accelerate a fuel injected car for it to start up

i have changed the ect sensor and camshaft position sensor
cleaned throttle body/changed fuel filter/plugs/oil clean ht leads

once the engine has been started it fires up first time, its just in the cold morning

i suspect a battery but its cranking fine

anyone who has any ideas please let me know

regards

Frank