One strategy I used to see recommended on the Alz. Soc. carers’ forum, was to write to the GP, saying that you understand that they can’t discuss a patient with you, but you are pretty sure there are signs of dementia. The person however will not agree in any circs. to see the GP on those grounds, but perhaps they could be called in for an ‘over X age health check’ where some suitably subtle questioning could be used?*
It’s as well to be aware, though, that a diagnosis doesn’t necessarily help much (if at all) and that any medication will at best probably only slow the progress down.
One practical thing to do, is to get powers of attorney put in place asap, if possible.
*also recommended was to accompany them at any such appt. (if possible!) and to sit slightly behind them, so that if and when they give any wrong answers (to e.g. ‘Are you still able to do your shopping/cooking, etc.?’ you can discreetly but firmly shake your head.