Having looked at all the all the new localgov site launches since April - Phil Rumens said he was looking for a way to find beta/test sites. Now the localgov speedy script takes a list of existing sites, and tests them, but it's not a huge leap to change the code search the sites we are looking at for signs of "beta", or "new website", so I created a new script looksy.py that did that.
It turns out that's not a very good way of finding a new site - after a few tweaks I found beta darlington.gov.uk so you could say that is the only public beta at the moment.
Undeterred I've create a new script guessy.py that just sees if there is anything at the end of a domain name. (i.e. takes darlington.gov.uk and looks for beta.darlington.gov.uk or new.darlington.gov.uk). and that works much better - I now have 14 local government beta or new sites. Now just because these sites say beta / new doesn't mean they are/aren't launched in some form (hence all these links are rel=nofollow)
Beta Sites:
Birmingham http://beta.birmingham.gov.uk
Cheshire east http://beta.cheshireeast.gov.uk
Darlington http://beta.darlington.gov.uk
Devon http://beta.devon.gov.uk
Gwynedd http://beta.gwynedd.gov.uk
Hounslow http://beta.hounslow.gov.uk
Wandsworth http://beta.wandsworth.gov.uk
South Gloucestershire http://beta.southglos.gov.uk
Barnsley http://new.barnsley.gov.uk
Brighton Hove http://new.brighton-hove.gov.uk
East Devon http://new.eastdevon.gov.uk
Lancashire http://new.lancashire.gov.uk
Shropshire http://new.shropshire.gov.uk
Telford http://new.telford.gov.uk
_if your website is on this list and you want it taking off - drop me an email and i will remove it (but you probably want better security on something you don't want people to see) _
Open source everything: At Jumoo, we open source everything, so even though the python script is a bit of an abomination, you can go to github and see for yourself what we have done to find these sites.