Coral artefacts are very uncommon in Britain [1][3], a single coral bead has been found in one burial site in the Battlesbury hillfort in Wiltshire [1], a coral artefact was also found at Maiden Castle in Dorset [1], a ‘fragement’ (possibly a bead) of coral was found at Danebury hillfort in Hampshire [3], and the most numerous finds have been at the brooches at the Wetwang Slack site in Yorkshire [1][4], among which included:
a brooch with three coral beads, a brooch with two coral beads that have been ‘replaced by iron oxide’, a brooch with a piece of pink or white coral, another brooch belonging to a female between the ages of 35-45 that is covered in coral pieces, and a final brooch with a coral piece secured by a bronze rivet [4].

As you can see, coral appears to have been used as a decorative object for brooches and pins [1], but again these items are very rare.

Unfortunately, we don’t appear to know who brought the coral to Britain. The coral bead in Battlesbury likely came from the Mediterranean, and probably arrived in Dorset before making its way to Battlesbury [2]. It is highly likely that this is an indicator of trade, although most of the goods in this hillfort did not derive from very distant locations (sarsen from east England, sandstone from south Wales, and shale from Dorset), they still demonstrate at least local trading links, and again it is probably from somewhere from the south coast of England that this coral bead originated from (after arriving possibly from the Mediterranean) [2].

The coral beads in the north of England are contained in early brooches that follow a continental Celtic style [5], indicating that the coral, along with bronze and glass, was a product of a trade route with the European continent [5][6]. For a time, coral seems to have been completely replaced in these brooches, along with bronze becoming less common. These brooches have an ‘increasingly insular style’, possibly indicating that this continental trade route had diminished, which resulted in a lack of coral imports and the necessity to replace these beads with glass [5].
Continental styles and coral beads once again appear in some later brooches, again lending further support to the coral originating from Europe, and travelling to Yorkshire along trade routes [5][6].

Occasionally in these sites, other valuable artefacts of trade can be found, such as three amber beads in the Danebury hillfort [2], or glass rings, amber, and jet (the gemstone, not the plane) at Wetwang Slack [7]

So, in conclusion, these coral imports were quite uncommon [1][3]. They were used as decoration in brooches and pins, largely following a continental Celtic style [5], and these coral pieces were probably brought to Britain through trade [2][5][6].
This trade likely originated in the Mediterranean [2], with these more exotic goods of amber and coral being brought to trade centres in the south of England, before being dispersed to sites such as Battlesbury and Danebury more inland via local trade routes [2]. This trade might not have always been strictly through Mediterranean ships, as the use of a continental Celtic style in the brooches found in the north of England also indicate trade links with the European continent (such as with Gaul) [5][6].

Bibliography:
Ellis, C., Powell, A.B. and Hawkes, J. (2008). An Iron Age Settlement outside Battlesbury Hillfort, Warminster, and Sites along the Southern Range Road. Wessex Archaeology Report, 22.
[1] p.50
[2] p.136
https://www.wessexarch.co.uk/sites/default/files/An-Iron-Age-Settlement-outside-Battlesbury-Hillfort-and-Sites-along-the-Southern-Range-Road.pdf

[3] Cunliffe, B. (1984). Danebury: an Iron Age Hillfort in Hampshire. Council for British Archaeology, 52(2), p.396.
https://archaeologydataservice.ac.uk/archiveDS/archiveDownload?t=arch-281-1/dissemination/pdf/cba_rr_052b.pdf

Dent, J.S. (1984). Wetwang Slack: An Iron Age Cemetery on the Yorkshire Wolds.
[4] p.160-165
[5] p.101
[6] p.135
[7] p.42
https://etheses.whiterose.ac.uk/1819/1/DX190573.pdf