For Queen and Country

You would have to get the Queen on side or at least acquiesce to stand even the smallest chance. If the Queen stands by Parliament the coup is lost. You might find a (very) few senior armed forces officers to join the coup but the rest and junior officers and the rank and file will side with Queen and Parliament, not to mention the Police. Rather than a civil war it would be an extended holiday on full board invitation by polite unarmed constables turning up at the relevant front doors. If the Queen denounces the coup then it is lost straight away.
And just for avoidance of doubt, you could replace those 'ifs' with 'whens'.
 
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