How long did it take to get your provisional licence?

I mailed everything first class on 3/10 and got my licence a week later on 10/10. My passport came a day or two earlier. 

I did special delivery both ways (£4 each way, but it was worth it for my passport). Mailed out on a Friday, got back the following Friday. My license was regular mail, my docs were in the special delivery envelope, and I got them back the same day.

First piece of ID with my married name on it, too 

As a follow up, I did ask for a free certificate of mailing at the post office when mailing my passport off.  If you don't get one, your compensation options with Royal Mail are more limited.  Based on my own experience, special delivery wouldn't be worth the extra £8.  I got my licence in the same amount of time as Stoatula (and I'm in central Scotland and the form goes to Wales). 

Is there any way of doing it without sending off the passport? Like going in person?

I sent my application in a Priority Mail envelope with a self-addressed PM envelope inside. I received my passport back in a week and half, and my licence a few days later, so roughly it took me about 2 weeks. I believe on the application it states to not send them your passport if you need it within a month. (In other words, don't apply until you come back.) I wouldn't want to scare you, but there are some who have had their items lost in the post, so I wouldn't take the chance.

Is there any way of doing it without sending off the passport? Like going in person?

If you're not a British citizen, then no.  If you are a British citizen, then there is.  Someone posted about it on page one.