Installer can be downloaded from Linnworks.net platform under Settings > General Settings > Desktop Application.
Unfortunately, the local versions installed is no longer available for quite a long time now. There were multiple notifications about the discontinuation of Linnworks Local at the time when it happened. All Linnworks databases sync via the cloud nowadays, hence why the installer for the current version requires an actual email and a password. The link Aleksandra provided you with is the only installer available and if you wish to use Linnworks you would require to register an account and login that way.
There is still an option to use a free version of Linnworks, however it has its own limits for obvious reasons. You can check the pricing options and their limits here: http://www.linnworks.com/plans-and-pricing
I do have a copy of that old installer that works with local SQL DB. Send me your details and I shall send it to you.
No longer available so we are a bit stuck
Any help much appreciated :)