Even Thatcher went to Parliament in order to pursue the Falklands War -- but then, she had the safety of a majority, I suppose (and, for the record, she also had the safety of being absolutely correct to want to go to war to defend British territory!).
For a single air strike, supported by allies, and with no apparent military follow-up, I am not sure that there's a need to consult Parliament, but certainly she should be prepared to defend the decision to them, and be accountable if they do not agree.
Otherwise, what is our democracy if not a joke, at the whim of only a single person or a small team? If we were to pursue further military action in Syria, of course it stands to reason that May should ask Parliament. Not only because in that case she'd be virtually legally obliged to do so anyway, but also because morally, aggressive wars ought to require consensus.
There's no need to pretend that Parliament stands in the way of defending our country if it came under attack, and it's a rather deliberate red herring on your part.
Also, for the record, I haven't any complaints about the British strikes per se. I just fear it's too little, too late, and I don't anticipate anything else to follow it. Most likely it's just an attempt to pretend that the West are doing something; there wasn't a follow-up to the Cruise missile strikes Trump ordered a year ago either.