Actually, in my opinion, celtic in Britain and Iberia arrived around at the same time, with the Late Bronze age upheavals (c. 1300 BC), when the Atlantic Bronze Age emerged. Here is a map of what I believe could be the Celtic Urheimat in the middle Bronze Age, the Tumulus Cultures (c. 1600-1300/1200 BC):
Note that the "Late Wessex and Atlantic Middle Bronze Age Groups" shown in the map are not what is now usually known as the Atlantic Bronze Age, which is now used only for Atlantic Europe in the Late Bronze age
Wessex is a Atlantic culture, curiously predominant in central and southern Britain, is linked to the armorican culture (prototyp with the Middle Rhine group Beaker culture and related with the NW Spain beakers) and had wide ranging trade links with continental Europe, the Baltic, Bohemia, other atlantic zones and the Mediterranean (in some galician petroglyphs we can see swords and daggers with this procedence) and was the intrusive Beaker group that appear in Ireland.
We can see the evidence of standardization the reiterative samples in all of the registers in the Atlántic Culture influence area, from hydronyms to place names. For example, the commonly name DEVA as a river name, that aproach us to some typical idiosyncratic of the Bronze Age. Rituals related with the rivers (sword deposits, saunas, profusion of deities related with the water in the historical times), that connected directly and ideologically with the concept of the warrior indo-european world.
It is not exists discontinuity not only in Western Iberian Peninsula, the same context is applicable to other Atlantic areas (British Islands, Armórica). The evidence is all material culture is definable EXCLUSIVELY inside the atlantic sphere or an hydronym sometimes indentical, even in its suffixing (-ia-, -io, -ara, -is-ya, -us-ya, -ona, -on-ya/yo, -ana, -an-ya/yo, etc.).
The oldest celtic word *okel(l)o- (< ie. *ok-el(l)-o-,synonym of *briga, *brigs, *dunum, *arcos and considerated as Ligurian in other times) is other example of this standardization language, that we can see from Utrecht to Britannia, Alps, Liguria, Celtiberiaand in all of the Wester Iberian Peninsula or in spiritual designations like the god Lug or the callaecian SULEIS (< *sulevis) with gaul.-brit. SULEVIA. Moreover, they are so fossilized that there is no way to deduce it as newest or coming with a secondary way.
Looking your map, we can see the real influences of the Corded Ware, Globular Amphorae and Comb cultures between the Odra basin and eastern Dnieper basin, in the pre-lusacian cultures of Trzciniec and Komarow and in the Estonian baltic area. It is visible for the trans-carpathian Bronze center of production of Thuringia and the ambar trade between the baltic/greek-anatolian routes and not in the mitic celtic homeland of Central Europe.
The incidence of this cultural influences spread to NortEasth, how we can see in this maps:
Interpolation der 14C-Daten für die Schnurkeramik des Mittelelbe-Saale-Gebietes mit Hilfe des IDW. Die geringe Höhe des mittleren Alters im westlichen Nordharzvorland und der Altmark ist sicherlich auf die geringe Datenmenge zurückzuführen, während der Unterschied zwischen einigen thüringischen Gebieten und denen am unteren Saalelauf offensichtlich ist. (Interpolation of 14C-data of the Corded Ware in the Central Elbe-Saale-region with the help of the IDW. The low average of the ages in the western Nordharzvorland and the Altmark probably results from the small sample size, while obviously the disparity in age between Thuringia and the lower Saale displays real age differences.)
Interpolation der jüngsten 14C-Daten für die eingezeichneten Regionen im Mittelelbe-Saale-Gebiet. Die gegenüber anderen Kleinregionen längere Dauer der Schnurkeramik im Thüringischen wird deutlich.(Interpolation of the youngest 14C-data of the areas which are marked in the Central Elbe-Saale-region. The longer duration of Corded Ware in Thuringia is visible.)