I advertise my availability is from 6am every day that I'm working, but they must book the night before, by 8pm, so that I know I need to go to bed earlier!
I always ask them to confirm half an hour before the booking is due, so then I set my alarm for 5 mins before confirmation time, e.g. if they're coming for 6am then I set my alarm for 5.25. I get up, switch my phone ringer on, then give them 10 mins to confirm. If they don't I switch the ringer back off and go back to sleep. If they confirm then I've got half an hour to get showered, shaved and made up.
I find early birds really popular in London but I also did lots in Brighton (where a lot of people live who commute to London daily.) But I get at least one every tour. I had two in Glasgow on Saturday morning, a 7am and an 8.30.