Long grass is not so much of a problem; at least, it keeps down dandelions.
The issue is the brambles you mention. Brambles are hardcore bastards, and when they get established, it is very difficult to root them out.
If you've any fencing or garden walling, brambles can become a major problem by undermining the structure. And unless you rip them out by the roots, the problem will come back year on year and get worse.
However, there's not much you can do as a neighbour. It's their land: their plants.
We are in a similar position, but our neighbours recognise they struggle due to family commitments and, as such, work with us to keep their garden from getting completely out of control, but your situation appears different.
Out of control gardens do become a health and safety issue eventually: undermining garden brick work, leaf fall in wet weather making paths slippery, trees growing beyond a manageable height too close to residential buildings, root systems undermining pathways etc. It can get very expensive to rectify if things get out of hand.
If the situation starts to affect your buildings insurance, I think you have to say something but until then, it's tricky.
You could, however, encourage a local gardener to pop a leaflet advertising services through their door.