I was driveing my mini cooper and the engine managent light came on then went out then came back on and the eml light came on as well and wont go out

misfires are also caused by low fuel pressure injector electronics faults and faulty injector tips . Replacing plugs is half the fix

You will need to go to a auto parts store and use their OBDII Reader.

Remove both battery cables, hold them together without touching the battery, for 30 seconds, then reinstall battery cables. This resets the ECU, then drive normal. See if it helps!

The following are descriptions from the Mini-Cooper S owner's manual.

Service Engine Soon "?If the warning lamp comes on
either continuously or intermittently, this indicates a malfunction in the emissions-related electronic systems."

EML light: "Engine electronics ?Malfunction in the engine electronics. You can continue to drive with reduced engine output or engine speed."

Triangle circled by an arrow: "Automatic Stability Control plus
Traction (ASC+T)/Dynamic Stability Control (DSC)
?Indicator lamp flashes: System active: drive and braking forces are regulated.
The indicator lamp stays lit: ASC+T/DSC switched off with button or defective. In the event of a defect: please have the system inspected at your MINI Dealer."

First, inspect the belts to make sure none failed at high RPM. If one broke, inspect any cable or hoses in the plane of the belt to see if there was any damage (e. g., a ripped wire in the ASC+T/DSC system). Second, get a readout of the engine error code. (If you get indications of a major vacuum leak including rough idle, look for a blown head gasket.) If you get something else, please post the results in a comment so we can go to the next step.

yellow EML is ok and will pass the car.

but EML is telling you there is a fault with engine.
although it will be ok for mot purpose but not for the car.

The Service Engine Soon is for an exhaust emissions issue and the EML is engine electronics. Could be a sensor or something else.

The service engine light is on because the ECU has stored a code. Have someone with a reader check the code to see what needs service.

Engine Management Light, same as a Check Engine Light... simply means a sensor component on your vehicle is malfunctioning You'll need to have someone with a tester to run diagnostics and retrieve codes to find exactly what the culprit is. Don't be surprised if it's the Throttle Positioning Sensor (TPS), common problem on BMWs

the engine control unit has detected a fault light illuminated which in turn reduces ability to gain high revs as a damage limitation exercise , known as limp home , car requires diagnostic computer to check fault codes to indicate faulty component causing ecu to go into limp home mode

Try reading the obd2 code with your phone and this cheap device