The A23, under the 26 approaches, is a public road so you are unlikely to be moved on if on foot, but I wouldn't want to spend much time standing alongside it. Plus there's a hedge between it and the perimeter road that makes it hard to see the runway (and the perimeter road itself is airport property, so it's possible, though unlikely that you will be moved on from there). If you just want flying shots, the cycleway between the A23 and the railway is good.
There's a good view of the approach and touchdown from the southernmost of the three South Terminal short-stay car parks (although you are south-facing). If you park on the top floor you'll be moved on PDQ, but on the lower floors the view is just as good and there's a reasonable chance that you will be left alone for a while. It's not cheap, though.