Range Rover TDV8 Non Start confusion

Good evening all. Please could I have the benifit of your collective experience.
Range Rover 3.6 TDV8 2007
So, in the summer with the car running like a dream. I went out to lunch, parked the car and returned about an hour later and it refused to start. It had all of the symptoms of a flat battery. Completely dead. I called the RAC and they diagnosed a loose connection on a battery terminal. They tightened it up and all was fine. ( I was a touch sceptical)
Spin on to tonight. Went out, car started and ran fine, no evidence of sluggish turn over when started from cold. Went to the supermarket for 10 mins, got back to the car and it really struggled to turn over and then failed to start. Clicking, rapid strobe from the headlamps when cranking but, all interior lights, headlamps etc all seemed to work fine. RAC out again and the battery terminals were tightened and the car jumped . It ran fine all the way home. (About 5 miles) when home, I tried to start the car again and nothing but a click. There is no alternator light on the dash. RAC man thinks that the loose connection has fried the alternator. Looking over his shoulder, it looked as if his meter was reading 12 ish.
Any thoughts? Many many thanks. As ever,
Charles.

You should be looking at around 14.5v at 2000rpm with everything on lights heater the lot.

Thanks. So you think the alternator?

I'd still look at the battery. They are greedy girls and like maximum juice in the battery. Loose connection first time is a fair answer, as you're not the first to have the issue. Had it myself in mine, even although she's earlier.
She may have been on the edge when she started for you to get to supermarket but a short run ate what was left and she couldnt recharge in that distance/time.
Getting her jumped and then only driving 5 miles home, again is not enough time/distance to recharge the battery. She needs a proper run after being jump charged. I'm surprised the RAC guy didnt tell you that.

Worth checking with the old multimeter, quick and free to do.

Thanks both, I am away from any tools or a jump pack so it will be an RAC trip to my local specialist tomorrow. This has been one of the most reliable cars I have owned dispite it’s 140k and, of course, servicing and fettelling constantly.

One quick reference, with the bus running, take off the black - lead. If it dies then the alternator isn't charging. If it continues to run the you could be looking at a battery fault. Do this very quickly as most alternators don't like supporting the engine so make sure all accessories are turned off!!