This morning started the car and received two errors on the dash
1) Restricted performance,
2) Charging system error.
I have a cheap voltage meter that fits into the 12v plugs inside and it reads only about 11.5v when the car is running.

What should my next steps be to diagnose?
What should I be looking out for? 2011 Vogue SE 4.4 TDV8

If you go to 2000rpm, does it still say 11.5v?

If so, it's probably time for a new alternator. The older I get, the more I realise that people confuse wrinkles for wisdom

+1 for alternator but I would check that the alternator is turning under full load, A mate recently changed a battery and alternator on a JLR car then found out it was a failed bottom pulley. I'm not sure if yours will have a damped pulley but it costs nowt to check.

Working on a bit of a process of elimination here. First battery, then other items.

I removed the battery and took it to a shop for charging that testing the health of the battery. It did charge, but the guy said that the SOC and SOH is at 70 and 80 per cent respectively (whatever each implies), but that the battery has about a month left on it.

Could a battery on its last legs cause these errors? 2011 Vogue SE 4.4 TDV8