My 10 week old puppy is starting to exhibit signs of separation anxiety. I work from home and basically, he can 'see me' all day when I am working. My office is next to my kitchen where the pup spends his day. There is no kitchen door, just a child gate between us. He is fine all the time he can see me but a couple of times in the last few days he has started to whine if I move from his sight (eg. to answer the door, hang washing out etc). However, he is happy to spend the night in the kitchen alone and without me in his view. I want to jump on this as quickly as possible, so can I ask how you would handle this please?

'Separation anxiety' although a reality in some cases, is a very over-worked term.   I suggest, as all dogs are opportunists, your puppy is just hoping that if he cries, you'll react and go to him.   He has to learn that there will be (hopefully?) a time for him, and a time that's not for him.   Make sure he's not asking to go out to empty, has been fed and as water available, and some toys, and ignore him.  You could have some music playing, quietly.

MB, I'd put it a slightly different way. Dogs are highly social animals, they are not really wired to readily cope alone and have to be taught this. So incremental separation training should be viewed as a vital part of puppy training, though it is not covered in many classes in the way it should be.

to the OP-

Your pup is simply exhibiting a normal biological response to you disappearing from sight, even momentarily. You are the centre of his world, his primary caregiver. You now have to teach him that there is no threat involved if you disappear and that you always return. As you are finding, disappearance from his sight for only a second provokes a reaction, that is your starting point. As MB suggests, handling this the wrong way can sensitise the pup to any separations and then you have the seeds of a problem. Key is ensuring your pup is relaxed and distracted by some great treats or a desirable chew, while practising brief departures.  It is important that your pup learns you are not on tap and so turning your active attention to him on and off is a first useful step, as is ensuring he does not shadow you and follow you from room to room.

The fact that your pup has been able to see you all the time, other than at night has set a kind of precedent for him of what is 'normal' and therefore safe, you now have to teach him that temporary disappearances and then more prolonged separations are also normal and nothing to be worried about. This will take TIME and conscience, consistent training sessions.

At ten weeks your pup may also be in a fear period when his developing neural networks start 'waking up' to potentially threatening differences in the environment, so having you around is more important to him, you if course being the big protector.

I'd find a good local trainer or behaviourist to do a session with you and show you the various steps involved. I believe that getting this training right is very important, especially with all the demands of the modern world.

This works if your into the crating thing, which I must say I am not (only for when essential), but I think confinement in a room behind baby gate is same principle

https://www.siriuspup.com/files/blueprints/07HomeAlone.pdf

http://dogtime.com/puppy-training-home-alone-dunbar.html

This seems a step by step approach:
https://rogerabrantes.wordpress.com/2011/09/06/teach-your-dog-to-be-home-alone-in-five-steps/

For little pups crate in a puppy pen can work well, can encourage pup into idea of settling in a safe area outside times of interaction, feeding, play, training, toileting etc..

Another thing is to get the pup used to being ignored for short periods so that he starts to understand he doesn't always have your attention.
When you are together in the same room/area do things that don't involve your pup and turning away if you are pestered for attention, it's useful if your pup has something to occupy him such as a chew or playing with a toy. If you rub a little peanut butter or meat pate into a Kong for him to lick out or look at the dried pieces of animal that the Zooplus website has to offer, smelly but very entrancing to a dog.

Pups need to learn they don't always have your attention constantly and learning that he will be ignored when you are together will help when you need to do your work in peace and that you are not always in sight.

Thank you very much for all of your suggestions. Some of which I was already doing and some I am now trying, so thanks for your help! My confidence took a huge hit earlier this year when I lost both of my older dogs within weeks of each other. I think it has made me a tad paranoid about doing the 'wrong thing' and doubt my own abilities to do the right thing! I can see from your replies that I was heading in the right right direction to get on top of this problem, so will stop doubting myself so much now! Hopefully, I can sort this out now but rest assured that I will yell if I need more of your help and idea's Thanks again x

Great post from freelancerukuk. 

All the posts were helpful Those that shared practical help and idea's were especially appreciated.