Starting a car takes a lot out of the battery. The alternator quickly recharges it but there's a short period, immediately after starting, when the battery isn't able to give of its best. If you've got an HT lead which has built up excessively high resistance (as they do over time), the battery won't be able to provide enough current (for that short period after starting) to fire the cylinder which it serves. Consequently, the car will be running on just 3 cylinders for a short while, which makes it sound like a diesel engine.
Get your HT leads checked. (It simply involves checking the resistance with a multimeter). A new shouldn't cost a great deal.
Chris