Ignition switch problem

Recently the alarm went off when unlocking drivers door and wife open passenger door at the same time. Switched-off alarm by using door-key. Now every time I unlock drivers door and open it, the alarm light comes on (steady) and when I turn on ignition, warning lights come on and then it starts bleeping and I have to use alarm-fob to clear, then engine ok to start. Have tried switching alarm fob on & off two or three times before turning on ignition, also just using key to lock and unlock but still have to clear bleeping to allow engine start. Any ideas ? Forgot to say car is MGF 1999 1.8 vvc

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