I have a 1275cc clubman, and havinga bit of trouble with starting her up over last couple months (hasnt been getting better

)
first problem (though it might not be a problem) is the fuel pump never turns off, i understand it is meant to prime the fuel line/reservoir and then turn off...i have left ignition on for 5 mins and the clicking never stops....this however is not the problem ive been having.
might be cause its cold but i have been having trouble getting the car to turn over after it has been turned off over night or for a long stretch. ill let the fuel pump work for a little then 20-30 seconds later i will turn the key. all i hear is the starter motor trying to turn the engine. after a few attempts at this the engine STARTS to get some fuel in and ignite that. BUT the wierd thing is a few tries after that (when the engine is almost kicking over) a fairly loud CLICK will come from the engine bay, then without fail the engine will roar to life after this click.
my questions are, what is this click, is there any reason it takes so long for the car to turn over (other than being a carbi) and should i investigate the fuel pump not stopping?
cheers for your time
Lachy