Pete, I can only speak from my own experience, the vast majority of which has been gathered while working on the wetter, 'Atlantic' side of the country - mainly Wales, Cornwall and Devon. Points that authors such as Peterken and Rackham make are often applicable to the drier side of the UK, and aren't always relevant to the situation down here.
Anyways, bearing that in mind, a lot of my work has been in Woodland management in one form or another, usually coppicing or coppice restoration, and wood pasture restoration. In Oak coppice, felling results in widespread seeding of Birch and Rowan on acidic, nutrient poor slopes, with the addition of Hazel, Alder, Sycamore and Ash on the more fertile slopes and valley bottoms. Established Oak coppice will come up through this, eventually shading out all competition (with a couple of exceptions!) as it closes canopy.
Work on Wood Pasture restoration is really interesting, an area I've recently finished consisted of very mature Oak (quercus robur) that had grown up in an open landscape to produce trees of a glorious spreading nature - but relatively short compared to 'High Forest' types.
The really interesting bit regarding natural succession has resulted after a change in management led to a cessation of grazing about 50 yrs ago. This has led to a 'free for all', with trees seeding everywhere. The result is a patchwork of different species, with the 'pioneer ' types mentioned above dominating as expected. However , underneath the Alder, Birch, Blackthorn, Hawthorn and Hazel, smaller Oak, Beech and Holly are coming through,.
If we could accelerate the process by a couple of hundred yrs, I would expect to see a landscape dominated by Beech, Holly and some Oak, leading to eventual dominance by Beech and Holly. These two highly shade tolerant species will come up through anything, with the possible exception of Sycamore ( but will outlive that!). Left unchecked, most of our Oak woods would evolve into Beech/Holly stands.
So how come more of our woods haven't evolved this way (and many have in Cornwall)? The answer lies in the missing component from so many of our woodland ecosystems - large herbivores. I run a small suckler herd for restoration grazing and the impact they have on selection of tree species is huge. Beech and Sycamore are particular favourites, and in winter Holly and Ivy, preventing their dominance and achieving a more 'natural' balance of species.
Well I appear to have rambled on a bit, but its a subject I find fascinating(clearly:blushing:). To summarise, Oak will grow up through many 'pioneer' species but is just as happy on open ground, whereas Beech will come up through absolutely anything bar Holly and other Beech - and in my experience actually does better with other trees to 'draw it up'.
Any other questions, fire away and I'll try not to bore the ass off ya'.