I1 ,R1a, Q arrived with the Vikings, ANglo-Saxons and Jutes
R1b arrived also with all these germanics but also with celts. It is about 50/50 of the Celtic S116 and the germanic U106 branches.
I2 is probably of palaeolithic origin from the south european expansion after the glacial refuge
G2, J2, and E3b probably came with the neolithic farmers, but also could be some minority of Roman presence.
I2 needs to be split into the different clades here:
M26 I2a1 was probably founded in Iberia and in most cases probably pre-Celtic in origin when found in Britain.
I2b1 can be both of Germanic origin [more Anglo-Saxon than Danish, Norse] and ancient, pre-Celtic origin. McEvoy and Bradley [2010] assign I2b1a largely to La Tene Celts.
L161 I2a2b-Isles was probably founded in northern Germany, and some of it dates back to the Neolithic [Nordtvedt], whilst some came later with Celts [Manco], and Anglo-Saxons [Sykes, Klyosov, Manco, Owen].
I2a3-Western is founded near north sea and was probably brought to Britain by Anglo-Saxons
I2a2a-Disles- is a tiny clade so far found only in Scotland and Ireland. Probably pre-Celtic in origin.
I2a2a-Dinaric- the true, south-east european I2a2 is absent in Britain.
Regarding R1b, most R1b appears to be of pre-Celtic and Celtic origin save for the following:
R1b-U106/S21 -in some cases it is likely Germanic but there is no evidence that it is always Germanic.
R1b-U198/S29- this rarer clade appears strongly Germanic as does S26.
Also, a recently-discovered 'Norse' form of R1b, tested for as SNP S182 by Ethnoancestry appears Germanic in origin.
I disagree with the 50/50 Germanic/Celtic scenario envisaged by some for R1b. I think it is far more likely 70 Celtic and 30 Germanic, at least in Britain.
Re I1 and R1a1 in Britain- these are clearly Germanic/Scandinavian when found in British men. R1a1 is more often or not a signal of Norwegian Viking origin when found in British men [Wilson], but Danes, Normans and Anglo-Saxons carried R1a1 too. I1 can indicate descent from Danes, Normans and Anglo-Saxons. According to Nordtvedt, Barac and also Tambetts, the 23 at 390 and 13 at 462 type of I1 is more likely to be Scandinavian in origin, and the 22 at 390, 12 at 462 form a more likely indicator of lowland Germanic origin [i,e, Anglo Saxon]. The latter form predominates in lowland Germanic countries and Britain.
As for G2, J2 and E3b having Roman connections, I see no evidence in the form of an academic paper to support this conjecture. However, there is strong amateur consensus that E3b, in particular, might link to the Romans in some cases. There is evidence from Sykes for a Neolithic origin for all 3.