Going to London when not being allowed in the Schengen area

The thing is that UK border officers probably will notice that you have been staying illegally in the Schengen area for some time (either through the stamps in your passport or simply by asking you). At this point, they will examine your case much more closely and might deny you the right to enter the UK based on a concern that you would do the same there (namely stay illegally). There is nothing automatic about that either way (e.g. overstaying in the Schengen area does not entail a ban from the UK), it's not part of EU (or, to my knowledge, UK) law but a judgment left at the discretion of individual border officers.

Someone more familiar than myself with the UK Border Agency practices and internal procedures might be able to provide an educated guess on how likely that is but I don't think that anybody can offer any guarantee.

One thing that you could do is to get in touch with the UK consulate to get their opinion on this and perhaps apply for a UK visa beforehand (unlike the Schengen area, I believe it's possible even if you don't need one by default). This would give you the opportunity to explain your situation and provide guarantees that you do not intend to immigrate illegally in the UK. Beside the costs of a visa application, the big caveat is that if this application is denied you will be in a much worse position to enter the UK at any time in the future.

Other “solutions” include going back to Brazil instead of the UK or try to do the same from a country less concerned about illegal immigration.