Your homesickness like normal - normal but horrible of course.
Keep busy, e.g. on the tube read a book to help with the panic attacks. Try to do different sorts of things and go to different types of places. It's possible if you do standard tourist-y things you'll pressuredly think "I
should be enjoying this, this is what people studying here, do." London is a rich vibrant city but it's easy to lose yourself in it.
[Try to] Stop talking to your friends at home!! It'll only make you more homesick, like those people who go home from college to their parents every weekend and never really settle in.
Wear
sunscreen.
Read justamom's good advice.