Thanks for your replies. To JohnHawk: not condescending at all.

PROBLEM NOW SOLVED even if the solution leaves me puzzled.

I use Firefox as my default browser.

When I fire up my Lightroom 5.4 like yours -  it more or less immediately comes up with the window

=============================================

5.5

• Support for syncing star ratings and custom sort order to Lightroom mobile and Lightroom web.
• Fixes for bugs introduced in earlier versions of Lightroom 5.
• Camera support for additional new lenses and cameras.

Current version : 5.4 (build 955652)

=============================================

and at the bottom right of that window there is a Download button. However, when I click on that it takes me in Firefox to Adobe - Lightroom : For Windows : Adobe Photoshop Lightroom 5.5 but when I select "Lightroom" on that page it takes me to Photo editor app | Download free Adobe Photoshop Lightroom 5 trial which contains acres of Lightroom ads but no "Download" button apart from the "Free trial".

I looked around to see whether my Firefox is blocking something but no success there. I also tried it with Windows IE by copy-pasting the URL from the Firefox browser tab to Windows IE. Same useless result as with Firefox.

Then, doggedly determined to try everything on an arbitrary basis, I changed my default browser to Windows IE and re-clicked on the Download button at the bottom right. Bingo ! Problem solved ! The old familiar Lightroom download page popped up in the IE browser, I clicked on Download, and it is now busily downloading.

So the SOLUTION for my Windows PC/Internet Explorer/Firefox setup but possibly not of use to others is to run IE as the default browser for the purposes of updating Lightroom. I have no idea why that works and copy-pasting the URL to IE doesn't but, heck, it works for me. As a senior surgeon once said to me "Don't think, my boy, it only inhibits !".

Again, thanks for taking time to offer solutions.