Time.

ps - Britain did not invite the romans in.

Rome invaded Britain because it suited the careers of two men. The first of these was Julius Caesar. This great republican general had conquered Gaul and was looking for an excuse to avoid returning to Rome. Britain afforded him one, in 55 BC, when Commius, king of the Atrebates, was ousted by Cunobelin, king of the Catuvellauni, and fled to Gaul. Caesar seized the opportunity to mount an expedition on behalf of Commius. He wanted to gain the glory of a victory beyond the Great Ocean, and believed that Britain was full of silver and booty to be plundered.....

Caesar's military adventurism set the scene for the second exploitation of Britain - by the Emperor Claudius...

http://www.bbc.co.uk/history/ancient/roman...stions_01.shtml

http://www.romans-in-britain.org.uk/ind_title_page.htm

and a good time line - http://www.historyonthenet.com/Chronology/timelineroman.htm

I agree with Uhmanduh and Airika that the archaeological evidence from tree rings etc could be the result of a natural disaster such as a volcanic eruption and that the subsequent effect on agriculture and climate could have hastened the demise of empires such as the Romans/Hittites/Akkadians (other factors - such as the invasions by 'barbarians' was also an undoubted factor).

However it is possible that the tree ring/ice core evidence could be the result of a more mundane cause such as the regular solar maximum/minimum (or even a combination of eruption plus this). I haven't tried to cross-reference the dates in question as I'm too lazy.