I agree entirely with Paul. 'Going into work' or, more usually, 'Going in to work' makes sense. It combines the 'to' of movement with the 'in' of the work environment. The double negative of 'It doesn't get me nowhere', like 'I don't know nothing', is extremely widespread in the everyday speech of, let's say, lower socioeconomic groups of English speakers. There's nothing specific to the UK about this, and it's just as common in the vernacular of the US as it is in Britain - just think of all the lyrics of popular American songs which contain double negatives. They obviously don't follow the rules of standard grammar, but it's very common to hear them. By using it in his/her writing, the writer trying to inject the flavour of everyday working-class speech into the text.

'Going in to work...' is correct, yes. I don't like 'into' written as one word like that, but maybe that is a case of style preference, I don't know. 'It doesn't get me nowhere' is a double negative, which as you probably know is not grammatically correct. It should be 'it doesn't get me anywhere.' But having said that, there are a lot of people who talk like that, particularly those from working class backgrounds. It's very rare to see it written like that though, unless the person is trying to capture how people actually speak.

Double negatives make one sound like an uneducated person. Avoid them at all cost.