[Ilya]

Hi, wjw.

Welcome to the ranks of posters.
Your procrastination pains are familiar to me. I've spent years in this state and I know how frustrating can it be. As far as I understand, your problem only manifests in your work environment, doesn't it. If this is the case, I'm afraid you are in a wrong field of work for you. Can it be the problem? Think about it. Do you like what you are doing. Was it something that you've always wanted to do?
If the answer is no, and you've chosen this work for money, or out of fashion, or because someone told you to, then what you are experiencing may be the sign of impending burnout. You body might be telling you that it wants to get out. Judging by the lack of hope in your words, getting out may not be a bad idea.
I might be wrong though. And it is just a time management problem.
In this case I want to comment on the few of your words, that caught my attention

I also know the textbook ways of getting round this but none of them seem to work.

That's a bold statement, but I'll assume that you've really looked through the most of the time management systems, tried them for a considerable amount of time and they didn't work. I also assume that you've tried GTD and it didn't reduce your stress.

Every mini-task I undertake, particularly if it involves talking to someone else, holds out the terrifying possibility that I'll have to do yet another thing. There seems to be no end.

No. Completing tasks does not hold the possibility that you'll have to do yet another thing. Completing tasks holds the absolute certainty that you'll have to do another thing. And then another and then another.
There is one task that reportedly is an exception to this rule. In my task list it is called "To die." Still, some people believe that even this task is not the final one. Besides, I'm very keen on procrastinating on that one.

What I'm trying to say here, is that the purpose of doing anything is not to end what you are doing. Reading news, and playing games also constantly provide you with more and more stuff for you to do. But that doesn't seem to terrify you. The thing that we all try to stop from happening as soon as possible is pain. Pain in the broad sense of anything uncomfortable. And if your tasks cause you pain - see my first paragraph above and get out of this job.

Our life in general and our job in particular are the endless chains of tasks. You can't stop it. You can't complete life early and rest for the rest of it. You can't finish your job either. If you don't have anything to do, you get fired.

I don't feel like ticking tasks off will actually reduce the pressure on me;

You feel, or you've tried it and it really didn't reduce the pressure on you?
In any case it's not necessary ticking them off, it's writing them down that can reduce the pressure.

there are so many tasks and no way to be sure I'm doing any of them right, and each one done less than perfectly just creates more and more.

How many tasks are there? My current task list is close to a thousand items. And I don't feel any pressure, because I don't have to do them all simultaneously. I'll be doing them for several years and I'm sure by the end of this list I will have as much tasks in front of me. And mind you, these ones are personal. My work task are just a tiny part of that list. I've worked in software development and I would be surprised if you have more than several hundreds of tasks in front of you at any given moment. Usually, it is much less.

And if I actually finish them I have to work out what to do next, which is even more terrifying.

What scares you? What is your fear? I think answering this question will be the key to solving your problem.

I get exercise, and I do a lot of the right things. But I still read blogs for an hour in the morning when I should be clearing the decks and getting to work. How can I change this?

I'm not sure that reading some well chosen blogs for an hour is a bad thing. Some areas of life are so dynamic, that you have to know what's going on, to stay competitive.
But if you feel that what you read is the waste of time but can't stop you can try one of these things.
Read your blogs through a reader that allows storing the feeds in an archive forever. I use Google reader for that.
This way you'll know, that even if you miss some entry you can always go back and read it.
Then take a break. Say, for weekend, or even for a week. Then look at what happened through the reader, preferably in title-only mode. Try to guess what the entry is about. Read only the ones that feel worthwhile.
Then on a second pass, read the rest. Think about how much useful information you've gained during the second pass. It might be much less then
you would have expected. This way, step by step, you'll notice that there aren't many news to track. For one event there will be dozens of blog entries covering this event from every angle. Do you need every angle? Or may be the original news source will be enough?

Also approach this habit from a daily routine point of view. It seems to me, that you've just conditioned yourself to read blogs for a certain amount of time at a certain time of day.
You may try a substitution trick. Find a useful activity of about the same length and schedule it for the same time. Say, schedule a meeting. Not very useful, but it doesn't matter. Do it instead of reading and then go on with whatever you do after you usually read the blogs. After some time, you'll notice that your routine has changed. It may not be more productive, but you'll know that you are in the driver's seat and can condition yourself to something else.