It is all too enticing to imagine the early English as a warlike people, sailing across the North Sea in their warships, coming to seize new lands with fire and sword. The literary sources do not seem to know of any other process by which the English came to Britain (see Gildas, 23-25; Bede HE 1.15; Nennius HB 36-49). Moreover, a willingness to accept literary sources as reliable in early academia, not just in Early Medieval studies, ensured that this narrative became entrenched in the popular imagination (although, this entrenchment is slowly being undermined by modern scholarship). The natural reverse of this idea is that the Britons, the people the early English were seizing their new lands with fire and sword from, were not as warlike, for, otherwise, they would have been able to repulse these invaders.
However, this formulation is severely reductionist, ignoring the socio-economic situation in Britain following the end of Roman rule. Other users have effectively described this situation and the new theories in many other answers, for example:
The current academic consensus, thus, does not lend itself anymore to 'warlike'-ness as an explanation for the invasion. Moreover, 'warlike'-ness is impossible to quantify, and it is impossible to say whether one population group was more 'warlike' than another. As such, I am going to rephrase your question slightly to 'How did the Britons and early English think about warfare?'
As I said already, the arrival of the English in Britain was portrayed as a military conquest, with the early English coming as mercenaries, and eventually turning upon their employers to carve out their own kingdoms. The source of this narrative in Gildas. As many other users have demonstrated, Gildas was writing a sermon, not a history, and was likely moralising rather than providing an objective account, much in the same way that the migration across the English Channel today is called an invasion, despite the people coming not being invaders, it is designed to instill fear. Later literary accounts were largely drawn from Gildas.
English literature does reflect a strand of warrior culture in early English society. Beowulf extolls the virtues of warriors, with the eponymous hero largely being a literary ideal. In the poem, "bravery and loyalty, unto death if necessary, are the greatest of virtues, and a heroic and loyal warrior will receive rich rewards from his lord" (Higham and Ryan, 385). Beowulf is set in the fourth-fifth century, but it was possibly an oral poem before it was written down, meaning that the poem reflects society at the time which it was finally written down, oral poetry being in a constant state of flux. When it was finally written down, that could be any time from the sixth to the tenth century. Higham and Ryan support a date before the ninth century as "a text that sings the praises of the Danes is unlikely to have been composed after the Scandinavian raids... in the ninth century" (384), but it is possible that it was written during the reign of king Cnut precisely to reinforce English-Danish positive relations. Regardless, Beowulf reflects a warrior-ethos in English society, at some point.
Other English literature also points towards a warrior-ethos. For example, in the Finnsburgh Fragment, warriors are commanded to "Grasp your shield, steel yourselves, fight at the front and be brave!" This language is representative of poetry extolling warrior virtues from throughout history, such as Tyrtaios, from Archaic Greece. Similarly, The Battle of Malden also promotes a warrior-ethos, with much of the poem given over to the 'heroic' last stand of Bryhtnoth's thanes after the death of their lord and the rest of their army has fled. "Then the proud thanes went forth there, the brave men hastened eagerly: they all wished, then, for one thing - to avenge their lord or to leave the world." So, it seems that there is a clear strand of extolling a heroic warrior-ethos in English literature. However, there is much larger corpus of religious literature that has no bearing upon such an ethos.
Surviving British literature is somewhat less reliable, with poems thought to be genuine early Medieval compositions surviving only in later manuscripts. For example, Y Gododdin, a British heroic poem remembering 300 warriors of the Old North travelling south to war. The poem must be set during the sixth or seventh century, but the surviving manuscript comes from the 13th century. If you consider the poem reliable, then you have a genuine poem demonstrating the heroic nature of early Medieval Britons, much in the same way The Battle of Maldon remembers the deeds of the thanes, with the heroes slaying their enemies and dying with honour.
The Book of Taliesin from the 14th century similarly records possible early poems. Of these poems, several are thought to reflect seventh-century British society, primarily the praise poetry of Urien of Rheged and his son Owain. From the praise poem Urien of Erechwydd we can see that a lord is considered to be a good warrior ("When in battle you rage there follows carnage") and generous to their followers ("Most generous men!"). Warfare in these poems appears to be primarily raiding, and we can imagine that Urien led many such raids, after which he oversaw the dividing of the spoils.
Thus, according to the literary record, both the English and the Britons put a high value on a warrior-ethos, their poetry reflecting a desire for their warriors to perform well, and likely acted as inspiration for such behaviour.