I recently went for a PhD interview at Cambridge, where I met this cute HB8.5. We talked for a little while, had good time. Then I discovered that she'll be in London (where I live) for another interview in the next day, and I suggested we should meet up. Before I could even say anything, she was giving me her number (first proper n-close - that was easy ). Within 30 minutes after she left, she already texted me confirming the date she'll be in London and saying she hopes to see me there. We texted for a little while, just general chit chat with some IOIs from her and from me. I was kinda superexcited to see her at this point.

And then, next day, she texted me that she's not coming to London after all. Now, I'm pretty sure she's not just flaking, but it really sucks, since she's from Edinburgh, and it is unlikely we'll meet anytime soon. Nevertheless, we texted for a little while again, got her SPAM (but then she's having internet issues so she's never online - I hope that is actually true) and that's basically it. I thought I can't really do much more at this point (bare in mind, I am still pretty much an AFC).

And today, I get a text from her asking me how I'm doing. That was pretty weird, as I thought that girls don't really start the conversations - unless it's an IOI. So I guess it's not over yet - but how do I proceed from now? The fact that she's pretty damn far away complicates it, and the only way I could do anything is by texting. Any suggestion/tips/routines/anything?

Reading the first part of your post, I thought to myself "she's a goner" but now that she re-initiates contact there is still some hope for you.

Problem is, you don't want a long distance relationship, trust me.

You also don't want to game her on SPAM. You do that in person
Use the interwebs for short conversations to keep a contact warm for you or to set up a date.

Only if you REALLY like this girl, pursue her. You can ask her if she's coming to london again anytime soon, and if so, that you'll show her around or something. It may seem a little AFC but this is not a girl you can take out with your friends because she lives so far away.

Personally I'd say, dont bother, there are a more women, closer to your home.