"If you're flying something like, for example a Luton Minor, that poodles along at 60mph and you have a bit of experience, there should be no great problem, or have I missed something"
At 60mph yes, watching out for pylons, towers, etc. But as FFF says, DR navigation will be correspondingly harder because the slow airspeed will give rise to huge wind (heading) corrections, say 30-40 degrees, for typical values of wind aloft, but the poor vis will make it hard to make the corrections.
Also 3000m vis will invariably mean no horizon. In the UK, it is either due to very heavy rain, or (more often) due to haze. In the latter case, you are flying in IMC in all but name. It's like being in an aquarium that hasn't been cleaned for a year. From say 3000ft, you can see the surface but only just, so unless you have instrument skills you have to be down (say 500-1000ft) and then you can't see far ahead to navigate.
During my PPL training, I was with an instructor who was a bit of a cowboy. He liked to demonstrate things like stopping the engine totally and gliding (C152). But he taught me a few good things, like flying in 3000m vis in drizzle, low down, between hills, and you quickly realise it's an easy way to die. It's easy to see how getting into that situation quickly becomes a fight to just stay away from terrain. DR nav, with its high workload, will go straight out of the window. If the poor vis is due to rain, there will very likely be low cloud (say OVC007) and then a pilot without instrument skills is stuck between ground and low cloud, with poor vis. I've heard it on the radio a few times and it is quite scary.
Like a lot of things in flying, it's OK in a familiar area, and this is the unstated perspective which a lot of people are writing from. If you did a survey of typical trip radius for 60mph planes, you'd see this
A GPS is the best way to navigate. VOR tracking is also fine (and is sort-of mentioned in the PPL) but if one is low down the reception might not work, so one has to fly higher and then (in 3k vis) you won't see much of the ground so you need reasonable instrument skills. DME reception disappears particularly fast when low down.