Moss or shrub ID (South UK area)

Question

I had been hiking between Seaford and Eastbourne in the UK. Basically just following the route at the edge of the cliff so this is a high-moisture area.

Having trouble understanding which plant it is. Thanks!

Link to Google Photos with all photos that I've got

Answer 1

The tight bunching of the flowers/foliage/bracts and indistinguishable flower parts sort of call for an Amaranthus (think Celosia cristata for example). Amaranthus is predominantly a tall annual but can produce very woody old stems that can make it appear to be a shrub, and in an exposed environment like a shoreline it can become more compact than normal. In addition amaranth is known for salt tolerance; many varieties appear in a Caribbean/African context. I scanned a few species but did not find anything suitable so I don't have much confidence in this suggestion but wanted to add it to the list.

Answer 2

This is a guess based on the first photo and the assumption that this photo shows purple flowers. To be sure we will need better photos or you have to do a comparison by yourself.

Thymus polytrichus subsp. britannicus (Wild thyme)

Noteworthy Characteristics

Thymus polytrichus subsp. britannicus, commonly called mother of thyme, is a creeping, woody-based thyme that is primarily used as a small ground cover, but also has limited culinary value. Numerous stems form a flat mat (2-6" tall) with tiny, rounded, fuzzy, blue-green leaves. Leaves are aromatic, but strength of scent varies according to habitat and season. Clusters of tiny, tubular, whitish to rose-purple flowers appear in early summer. Unlike the species, the stems of this subspecies are hairy. Flowers are attractive to bees. Plants are evergreen in mild winters.

(emphasis mine to help identification)

The identification has partly been based on Bing Visual Search and especially on this photo.

A possible confusion is

Large Thyme Thymus pulegoides does not throw out runners and has elongated whorled flower spikes

and Thymus pseudolanuginosus (Wolly thyme), which I think is more related to Southern Europe.

UPDATE two new photos added:

The flowers on the new photos do not resemble flowers of the Lamiaceae family which contains thyme.

It is more like the flowers of Boraginaceae. E.g. Echium plantagineum.

Echium and especially this species common in Southern England matches your photos and description in several ways. It has purple and blue flowers on the same plant and the flowers are often as plentiful and vigorous as it look like they have climbed or overgrown another plant with long and narrow (lanceolate) leaves. And old flowers forms "dead" areas. This is a good example of how this species sometimes is almost flowers only.

Look for long and narrow leaves and perhaps your phone/camera has a macro function.