I brought a new battery for my car it started ok within a few days it needed charging, soon as l removed my foot from accelerator the engine went out now it won't start with Jump leads even.

The battery light would have come on as soon as the engine stopped turning. The light means the alternator is not charging the battery.
You'll need to check fuel pressure and other factors to proceed.

Lead acid batteries don't like being discharged flat, and it could now be damaged and unable to hold a charge. It does sound as though the voltage regulator part of the alternator is allowing discharge to ground when it should not. You would seem to have a good warranty claim on the battery given they did check the alternator and pronounce it OK.

If you can drive it to Autozone,they will test your alternator for free,only takes a minute.Here's a link on how to remove your alternator.

The charging system on your vehicle is computer controlled . Your vehicle is a rolling computer .The instrument cluster has a microprocessor inside , there is also a body computer ( SJB ) smart junction box , Engine computer etc... they all communicate on a serial data network , C.A.N - controller area network . It's hard to know what's wrong when you don't know how it works . There could be codes stored in the computers , these will not always turn on the check engine light .
Ford Smart Charge System Alternator Not Charging
How to Diagnose Controller Area Network CAN

There is a diode in the alternator that you fried the instant you disconnected the battery....go get a new alternator. This was an acceptable test on much older cars, but not these days......

It sounds like there is a problem with the Idle Air Control (IAC) valve. Its job is to open and let air into the manifold when the throttle is closed at idle. If it does not open, the engine dies at idle. The IAC is mounted on the throttle body. Possibly the valve is clogged or stuck, in which case it could be ok again if it is removed and cleaned. Or it is broken, and needs to be replaced. Or, there is a problem with its electrical connection, that needs to be traced. Good luck, let me know if you have any questions.

1- For the overheat, remove the thermostat to run for a few days to see the problem come back. When the engine runs at iddle, press the upper hose connecting to the radiator to see there is a water flowing inside. a- IF there is then your water pump is OK. After a few days, put back the new thermostat to run as normal. b- IF there is not then you need to replace the water pump first.
2- For your battery draining. a- IF you change only the starter, then the solenoid is the culprit, not the battery, not the alternator. b- IF you have changed both then I suspect the diode in the starter and the battery. c- To determine which one is in item b, take off negative battery cable for 2 days, - if there is no problem when hooking back then alternator diode is a culprit. - if there is a problem when hooking back then the battery is a culprit. Good luck.

We had the same issue with our 2007 Yukon Denali XL. Died on us twice after sitting for short periods of time; once we watched a DVD with the engine off and battery died within 10 minutes. The dealership kept it overnight to troubleshoot why the battery died so quickly. They said the radio was "pulling" too much from the battery. (They supposably fixed it) But again a few days later the battery died again after sitting overnight. We brought it back to the dealership and they brought in a GMC "expert" to replace the entire DVD/CD/Navigation system. They also replaced our battery with a much larger battery, similar to the ones that GMC puts in there diesel trucks. They had our Denali for 5 days, but it appears to be fixed now.
Getting it fixed correctly wasn't without headaches, but it was all covered under warranty, including the battery. And they are updating the nav w/ the new edition disc as well for no charge.

Ok here is a little trick my dad taught me, turn the key til the battery starts but not the engine, so right before it turns over, do it 12-15 times and then try starting it, if it works then the fuel pump may be bad..

It sounds as if your alternator may have gone out. If you take the Yukon by an autoparts shop (Checker, Autozone, etc.), they can run a quick charging system test for you. Good luck!