Well, always a bit of a tricky genus. One of the things I should always do is to check that the plant isn't hairy at a fairly early stage, and whether the flowers are a rich golden yellow or a paler more acid level of yellow.
At least partly in retrospect, these flowers in Dene Park are a golden yellow, and the petals are longer than the sepals.
In this case I did remember having looked at the leaves to see that they were perforate, to check to see if there were any black dots around the edge of the underside of the leaves and petals - there were. This isn't unfortunately a character! The stem felt round with two small but clear ridges. In theory this species can be up to 80 cm tall, but is often less.
My next step was a bit more solid, to check the sepals which were actually pointed (rather than blunt), but without any obvious stalked black spots (although there could be some according to Stace, generally un-stalked). This is now beginning to look like perforate St Johns Wort,
Hypericum perforatum.
There were no black streaks or splashes on the petals, the stems were not squared off, there were "perforations" in the leaves, and the soil wasn't notably damp, the sepals weren't spotted (often in lines) and unequal (?), so it doesn't look like imperforate,
Hypericum maculatum ssp obtusiusculum, which I think I might have seen down towards East Lock perhaps - but its actually very rare in Kent.
The plant did not have a stem that was reddish with four wings, and the flower was not notably pale, with the petals only a little longer than the sepals, very few perforations, so it was unlikely to be the Square-stemmed, sepals also not very stalked-dotted,
Hypericum tetrapterum.
The plant didn't look a bit like
tetrapterum slightly four edged, but with sometimes red-flushed bright yellow flowers, wavy leaves with plenty of perforations and black dots on its pointed equal sepals and possibly elsewhere, quite rare in marshy places, Wavy St Johns Wort,
Hypericum undulatum. Not in Kent.
The plant wasn't erect but downy, with roundish stem, longer and more strongly veined leaves
with perforations, paler yellow flowers and fairly obvious stalked black dots on the sepal (and possibly also sometimes petal) edges, so shouldn't be the Hairy St Johns Wort,
Hypericum hirsutum. Mainly on chalk.
The plant wasn't downy except on the upper surface of the leaves,
with longer strongly veined leaves, but
without perforations, although similar paler yellow flowers and obvious stalked black dots on the sepal edges, so shouldn't be the Pale St Johns Wort on calcareous soil,
Hypericum montanum. Only West Kingsdown and Darenth.
The plant wasn't in an acidic bog or marsh in the west of the country, with procumbent stems rooting at its nodes, grey woolly-hairy almost circular leaves, and with sepals with reddish dots on the edges, so it wasn't
Hypericum elodes. Only Hothfield and Bedgebury.
There is the very erect slender-stemmed species with blunt oval leaves with cordate bases and perforations, petals orange-yellow, with reddish undersides, with black stalked dots on the edges of the petals and the sepals,
Hypericum pulchrum. Woodland rides and sandy heaths. Hopefully seen on the grassy area at Dene Park.
Equally the plant wasn't creeping across the ground, smaller oval leaves, with smaller pale flowers, petals a bit (but not twice) longer than sepals, "normally" dotted sepals and a round but two-ridged stem, so it wasn't
Hypericum humifusum. I think I have seen this on the sandy soil at Pembury.
There is the rare toad-flaxed leaved species,
Hypericum linariifolium, upright, round un-ridged stem, longer, more linear leaves with very few perforations, petals more than twice length of sepals, lots of stalked black spots on sepals, Southwest and Wales on acid rocks, so obviously not in Kent.
That looks like all the reasonably likely herbaceous
Hypericums!