I just spent ages on line with Adobe technical support.
The bottom line is that the (two!) downloads that I did of LR 4.4 were both corrupt (presumably leading to the "unsafe" warning message).
This prevented the 64-bit installer program from being extracted from the download.
I've downloaded it yet again today and despite the file size being identical with yesterdays corrupt copies, it installed correctly.
To those that are still having problems I can only suggest that you download the 4.4 release version again and re-try the install.
Please report back with stories of success or failure.