Got the battery replaced last week as wouldn’t start and needed jumped a few times. Cold frosty morning and again won’t start. Please help ?

Could well be heater plugs/ relay as modern high pressure diesels rely on plugs far more than their older counterparts. You really need to first of all check that you're getting 12v (slightly over 12v actually) on the heater plug wire when the plug symbol appears on the dash. If that's OK, it's a matter of testing individual heaters although you'd be more likely to have  lumpy start if just one plug was down so I'd suspect fuse/relay / bad connection so long as it starts OK when not cold.

Modern DI diesels don't need plugs to start until well below 0c, they're mainly used for emissions reduction and a smother idle now.  It's the old IDI's that needed plugs to start even in fairly mild temps.  The light also has no relation to the plugs, they stay on long after the light has gone out.

 

What is happening when it won't start...does it turn over at all?  Does it start immediately with a jump?  Was a cheap (wrong) battery fitted?

I was led to believe that modern glow plugs heat up very quickly and so they're not as overt in their operation hence why people think they're not needed. With the bit where they stay on much after the light is out, is the plugs going onto a low-power setting which is as you say for emissions and smooth running.

I have a 2011 Ford Kuga (wifes) which I bought new in Nov of that year. After a year or so it would drain the battery completely and wouldn't even have the power to open the doors. Once jump started the issue would go away. This happened about once a  year and we lived with it. Last year however the problem got worse and the car refused to start on two occasions in a month. The AA were very unhelpful and refused to come to the aid of my wife and 9 month old daughter and left them stranded. Thanks AA. The battery was replaced and this seemed to solve the issue. Touch wood. I will say though that I got a bit paranoid about the issue and started the car before leaving for work,(in my car) to ensure it would start for my wife when it was time for her to leave for work. I started the car at 6:30am no problems at all, but when she got in it at 8am the battery was completely flat. I have heard if the vehicle is keyless and the keys are near then the car can search for the keys thus flattening the battery. We no longer keep the keys in the back of the front door and as yet have had no further issues?