I don't think that there would be any requirement to seek parliamentary approval prior to committing any UK personel to an Op, embedded or otherwise. I realise that this has been an evolving SOP of late - but that doesn't change the fact (constitutional ninjas tighten me up if I'm wrong) that parliamentary approval isn't needed. Usually there's a debate, but there doesn't need to be a vote. The government can commit the military without recourse to parliament.