Assuming the sample is actually representative of UK broadband households, i.e. not skewed, a sample size over a thousand is absolutely fine. Most reputable opinion polls are there or thereabouts.
What I don't get is the calculation of 136 respondents divided by 1,176 households. Was there just one respondent per household? Was that person responding on behalf of all the householders? That calculation could be overstating reality by a factor of 3 or more.
Were respondents asked if they *illegally* shared files, or just if they used file sharing software. The two are not the same thing.