If it can help :
I start in the morning and go through my mails, sort emergencies, respond, clear the stack completely before I start my day. Try to keep it under 30 minutes. If an answer deserve more attention I make a task of it and put it on the pile. Anything unanswered becomes a task to be tackled after lunch (see below). I must say I have the benefit to work in a radically different timezone than most of my correspondents. This allows me some leeway as they do not expect an answer until the next day. Also once I get through the daily mails I rarely receive any past 9am so I do not have to worry about interruptions from mails. However, I did find that this made me much more efficient so much that when get back in normal 9-5 rumble I will say that I only answer mails between 08:30 and 09:30 and between 13:00 and 13:30. I get some heat for this sometimes but they adapt, I even got a thanks once from someone that adopted this practice and nearly tripled his productivity !
Then I pick a task and work on it until it is finished. I tend to make my tasks such that they represent work units of 4 to 8 hours each, anything more deserved to be broken down further.
Lunch interruptions, log book brain dump, belly filling. Reading through blogs and keeping questions up to date on the few SE sites I keep close.
Then go through the task piles and fix low hanging fruits. Sometimes a task only requires a few minutes, analyse bug trace from support, help QA with questions etc. I find it harder to concentrate right after lunch so this time is perfect for such small tasks. Usually 1 to 2 hours devoted to this. Here it's not priority so much as the desire to get as many done as possible.
Then pick a new task on the pile and work at it until finished. Very often the same task spans the whole day with the extended lunch interruption (for the smaller tasks). possible also that I have to continue the next morning.
Any time I interrupt a task for longer than 1 hour I pickup the log book and make a brain dump of it there so that the time to get back in the zone gets shorter the next time I tackle it.
I find this routine suits me well and provides a healthy mix of allowed interruptions and long stretch to get in the zone.
Your Mileage May Vary