Fiesta cutting out problems.

Hi. I drive a Ford Fiesta 1.1 L 'reg' and its a fairly reliable first car. But recently the engine seems to cut out when you come to a stop, e.g. junction. I was told changing the spark plugs might help, but that hasn't stopped the problem, changed the oil too. Even when the engine has been running for a while and is at an optimum temp' it still cuts out, or tries to. Also when you dab the accelerator you can actually hear/feel a 'throaty' sound that doesn't sound normal, so I thought it might be an exhasut problem. Other than that it runs fine and bizzarely starts first time even when cold!