This gadget seems like it might be useful. I wonder if it will become available in the UK
https://www.petsafe.net/blog/2014/03/09/petsafe-is-proud-to-present-the-autotrainer/

There's something similar already available -
http://canineconcepts.co.uk/en/dog-whistle--distance-training/3036-manners-minder-remote-reward-system-759023080734.html

I already have one of those actually and do find it useful for some things. The petsafe one works independently of you and rewards the dog for not barking so would be good for separation anxiety.

The petsafe one works independently of you and rewards the dog for not barking so would be good for separation anxiety

Petsafe is a good manufacturer with a long standing history, this product sounds like it would be effective in some cases for nuisance barking in owners absence.
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There's something similar already available -
http://canineconcepts.co.uk/en/dog-whistle--distance-training/3036-manners-minder-remote-reward-system-759023080734.html

I looked to see who the manufacturer was for this product but could not find who makes it, do you know who the manufacturer is?
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Hmm, pretty pricey, but I wonder if it would help with my screamer! I have one who makes it almost impossible and a real embarrassment to take to shows / rally trials as she screams if I even look like I'm leaving her in the crate, even with the other dogs and a pigs ear etc. Let alone if I actually need to take the other dog away to work her! Something that will remotely reward her for not screaming while I'm not around sounds like a great idea!!

but I wonder if it would help with my screamer!

I doubt it very much, your description is that barking is a very intense 'reinforced' behaviour with your dog, that said why not call a retailer (if on sale here yet) & see if you get a full refund if it dont work in 7 days, if so nothing gained nothing lost but this is a new product & its effectiveness  over a wide spectrum of dogs of different types is not very well known yet.
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I have a small dog who barks when left on his own (its not separation anxiety as he's happy to be left on his own when it suits him) so I bought the Manners Minder as I thought it would be useful to be able to reward him remotely for not barking. Unfortunately the mere sight of it makes him bark with frustration as he knows there is food in there but he can't get it. An expensive useless gadget - for me but it might work for others.