Jaguar Repair Problems? Ask a Jaguar Repairs Expert.
Is the sound coming from the engine area? Could it be a squealing belt? Try putting the car in natural and revving the engine. This will isolate the sound to the engine. Then just have someone listen to see if they can pinpoint the sound.
It is doubtful that the battery is related unless the noise is a failing bearing in the alternator. The only way and oil change would cause a noise would b if not enough were added back in. I'm sure you've checked the oil considering you just changed it. It might be a belt roller or even the power steering pump. It would be a good idea to check the power steering fluid. Your pump will make a nasty noise if it is low.
If that doesn't do it, you'll need to isolate the sound with a stethoscope while the engine idles.