There is a lot of debate at present in Anglo-Saxon/Britich ('Celtic') circles with regards to who, when and where they were. Whilst Gildas says that they were 'invited' here to help out with problems the Britons were having with the Picts and the Scotti, the archaeological evidence shows that they'd been settle here since the end of the 4th Century and possibly early.
There is a great chance that it was the rising sea levels of the 4th and 5th Centuries that may caused them make their ways to our shores in greater numbers, but as to their expansion west, there is growing evidence that it was as much a cultural one as a mass migration with possibly even some British choosing their culture.
Far be it from me to correct Dave, but the Northumbrians were Angles, not Jutes... as far as I'm aware. The Jutes are thought to have taken the area around Kent and the Isle of White and parts of Hampshire. In fact there were other Germanic tribes, such as the Franks and Frisians, but they don't tend to get much of a mention.
The Midlands too were ruled by Angles, giving it the name of Mercia. So the six great powers came to be those of Northumbria (of the northeast) , Mercia (of the Midlands), Wessex (of the south), Kent (of the southeast), Essex (of the southeast) and East Anglia of the east. This left the Britons in what is now Scotland, Wales and the southwest (Devon and Cornwall). It used to be thought that they'd all be 'pushed' back to these area, but, as I said above, the theories behind this are changing. It was the Anglo-Saxons who gave the name Welsh, which roughly means foreigner, but in a rather nasty way. This is why those from Wales prefer Cymru, which means companion.
During the Arthrian Age the Britons seemed to have been spending more time fighting one another than the Anglo-Saxons and later we know the British and Germanic forces would join to fighting other Germanic tribes. It's possible they did this in the 6th Century but we just don't know. Maybe the Britons wouldn't consider the option until the Saxons had become Christian like them?
There are heated debates going on as to just how far west the Angles had come by the beginning of the 6th Century. Some dates are flying out of the proverbial window as Germaic finds are being made in places in the west of England they just shouldn't be for the dates they're being shown to originate.
The shires actually stem from the Normans - based on the Saxon model - so any county, such as the one I live in, Shropshire, was set up by them. Names such as Essex, Sussex, ect, come from the Saxon kingdoms.