Revision (i.e. change of view):

I have not got time right now to pursue this further. 

But until we can get accurate estimates of the population at the end of the Roman times, from land use and other studies, it would not be possible to produce an accurate model of what could have happened?

Is there a reference for this? Surely, somebody has looked into this? 

If the population levels are much lower than some people have estimated, the Roman occupation could have more profound affects on language change as well. 

Hypothetical.An attempt to refine the population model so it would fit in with the linguistic theory:

Population of Britain in 5th century = 1,200,000

Population of Sussex = 20,000(but this would only be a 60^th of the British population)

Immigrants to Sussex = 4,000 over 100 years(x 60 = 240,000, probably only settled in half of Britain so the estimated immigrants numbers could be just 120,000, or a tenth of the British population.)

Immigrant Population doubled every century = 16,000

Native population reduced by one third in the same period = 13,000(round down from 13,333)

Proportion of Germans =over 50% = enough? for a language change according to 

the linguists theory. The linguists really want 70% majority if words are not be carried from the old language (Brythonic) into the new Old English.  The actual percentage is 55% to 45%.

Now, suppose of the 13,000, only two thirds spoke Brythonic (8500) and the rest spoke Latin (4500).

The percentages would then be German 55%, Brythonic 29%, Latin 16%.  So the non-Brythonic (first language) speakers would be 71%.

However, I have just discovered a fault with the above figures which show a 50% increase in overall population and the land is unlikely to have supported more than 15% increase.  So this means the population of Sussex can only be 23,000.

If the Saxons did not breed so fast and there population only rose to 12,000. And the local Brits suffered an epidemic and their numbers were further reduced to 11,000, Brythonic 7000 and Latin 4000.

The percentages would then be German 53%, Brythonic 30%, Latin 17%.  So the non-Brythonic (first language) speakers would be 70%.

Estimated population of Britain in 1650 = 5.7 million

Sussex population = 80,000

(These figures have not been double-checked)

Although I started off being sceptical that the Germans would not be numerous enough to replace the Brythonic language when this proposal was suggested to me, it is possible that this could have happened.

My original was thinking was that post Roman Britain was bi-lingual and I think if anything the various views and thinking have strengthened this view. 

If the population in Sussex was higher, say 40,000, the immigrants could have risen to 16,000 and the natives fallen in numbers to 26,600, which would fit the Y chromosome genetic DNA research figures.

It is easy to get muddled up with figures. By increasing the number of immigrants it is well possible to make the linguistic model nearly work (which was not what I thought at first!).

What does not seem to have happened is that the Germans got assimilated into the native population as some historians say. It was a political takeover involving violence and replacement. But I would say there greatest success could have been breeding. Having displaced the locals of the best land, they became a more biologically successful group (especially the males).

I think I made a mistake with the previous model because it was not sophisticated to allow for spread, the snowball effect, inasmuch the immigrants would have settled the east, south coasts and Thames valley and half of the British population would be living elsewhere.

So if I was divide Britain into two parts, the Brythonic speakers living in their place name strongholds and the Germans conquered the other half, they would only need half the numbers to bring their percentage up to near the linguistic model.

My conclusion:In 200 years the German immigrants (maybe only 10%) transformed a bi-lingual Romano-Brit culture with Celtics into the English culture. The principal method was displacement and occupation of the best lands requiring force. Their success could be because of their greater biological success than the natives.

This is speculative; the experts in population studies must have got this down to an art form. I have not read the books though.