I'm actually doing an exam on this in two weeks time (A2 Classical Civilisation), the answer really depends on where, when and who you are talking about. The elites of Roman Briton (Curiales class) who occupied the towns and villas were certainly romanised even taking Roman names and depicting classical scenes in their homes. The rural population, are typically regarded as not being romanised, life didn't change for them and they farmed the same as their great grandfathers would have although perhaps agriculture may have been centralised there is little to no evidence for this taking place. Similarly, the tax system may have affected the rural population yet again there is little or no evidence for this taking place. The 'urban' population had to become romanised to advantage from and live within Roman Britain, the rural population were not affected, if so only slightly. It also depends on where, the South of England was certainly more romanised than the North because of the cooperation of the Southern tribes and places such as Cornwall that has Roman milestones, would certainly have not been romanised because the Romans had no interest in it economically or militarily. In terms of when, in the third century when the rest of the empire was in disarray, Britain flourished and was also split into provinces, perhaps giving more central control over the British people. Walking into the towns would be a complete culture shock, they'd be speaking another language and act a strange way and it would be nothing like your life in the rural population.

Sources: Roman Britain: A New History by Guy de la Bédoyère [Thames and Hudson]

Anyone interested in reading a thought-provoking re-examination of the concept of "Romanization" should check out David Mattingly's Imperialism, Power, and Identity: Experiencing the Roman Army (2011). Mattingly's focus is on identity (imposed, self-created, etc.) and on the relationship between people and power (in this case, the relationship between Rome and its conquered peoples).