Hi! My husband and I moved to Edinburgh last year the very beginning of September. Our lease actually started at the end of August. We came at the end of June/beginning of July on a flat-hunting trip. After emailing back and forth with several property managers, we learned that things only come up for rent about 4-8 weeks ahead of time here. We honestly didn't have a problem finding a flat when we came to visit. There were plenty available with leases starting in August.
Are you looking for furnished or unfurnished? Furnished are much easier to find around here, but also tend to be snapped up more quickly. We were looking for unfurnished and, although there were not as many, we found that they stayed on the market a little longer.
It helped us to contact a few property managers and set up appointments before flying over here, although I should warn you that most were uncooperative and we had some "forget" appointments when we showed up in their offices. We had good luck working with Hadden Rankin. They don't have properties on their website, but they have properties listed on
http://www.espc.com/EspcPublic/UniversalPages/HomePage.aspx They also sent us a list of their current available properties right before we flew over, so that we were able to set up appointments for specific properties.
I agree with Ian about the public transportation being very good here. My husband is a lecturer at the University, but we live north of the Royal Mile, in Stockbridge. It's a 30 minute walk for my husband and, although he has the option of a bus to take him right to campus, he always walks.
We are really cautious folks and didn't want to move over without having a flat already lined up. But there are so many furnished places that are advertised as being available now, that you may be fine with just moving over. There are several people in my husband's department who moved straight over into a furnished flat for the two months until their furniture arrived, and used that two months to find a more permanent unfurnished flat.