What is the proper email etiquette when contacting potential supervisors on short notice?

I am currently an MSc student in the UK and am hoping to apply for PhD at the same institution. I have found some potential supervisors but was wondering what is the correct way of wording my email given that I have only about 3 weeks till the application deadline and it's currently the holiday season (end of term). Some things to note: 1) my current field of study is immunology and I'm hoping to apply for a PhD in Medical Sciences, 2) it won't be possible to meet the supervisors in person since I'm back in the States for the holidays.