Peter Trudgill and Robin Lakoff

Peter Trudgill

Peter Trudgill investigated the ways in which speech varies among different people. He studied that the final consonant sounds in words are different depending on where you are. For example, in Standard English; the -ng sounds on the end of words are frequently used but in Norwich it is rarely used, and just a -n sound is used, in words like "walkin'" and "talkin"
But this isn't just used in Norwich, he studied. He found that higher class/formal areas or people are more likely to use the -ng, while less formal and lower classes use -n on the end of words.
He also found differences between male and female speech, like nonstandard -in' forms occurred much more often in men's speech than women's, and this was true for all social classes. 
Women liked to think that they said the -ng' form a lot more than they really did when questioned about what they said. While men stated that they used the -n' sound more than they really did.

Robin Lakoff

Robin Lakoff was a professor of linguists in California and developed a lot of books and accounts of women's speech. She made conclusions about women's speech, that they use a lot of: 
Hedging: using words like "kind of" "sorta
Polite terms: "I appreciate it" "would you mind if"
Tag questions: "You're going to dinner, aren't you?"
Use direct quotation: men tend to paraphrase more.
Apologise more.
Speak less frequently.
Use more intensifiers such as "so" and "very"
Lack of sense of humour: don't tell jokes and don't understand punch lines.
Use coarse language.
Use indirect commands and questions .
Have a special lexicon, women have more words for feminine things.

Language and Gender

In my opinion, there are noticeable differences between the socially acceptable way that both men and women talk, like there are certain expectations they should be satisfying. For example, I think it's never been very acceptable for women to swear, but men have always been more allowed to do it. In school, a male would always be typically punished less if they swore, than a female. This is also a well known stereotype that men do swear or use language profanity a lot more than women, but is that necessarily true? It is seen that more women than men tend to also cover up or sugar coat their swear words, like using "oh goodness" instead of "oh god" to avoid blasphemy or offending anyone. This then also links to the overall general stereotype that women should be more polite than men, using the umbrella term as "being lady-like" linking to sexism and what is expected of them.
Not only due to the spoken language, but women are usually permitted to cry in public and express their emotions more openly. In Key's observation (1975) that "if a woman cries into a pillow, it's 'muffled sobbing' yet if a man cries into a pillow, it's 'blubbering' with negative connotations".
Several writers have also stated that men will use a lot more colloquialism than women, such as shortened words and acronyms, as well as general slang. This was illustrated by the writers Labov (1966), Levine and Crockett (1966) and Trudgill (1972) the latter, who also noted women maintaining standard English more than men, in regional areas and their accents.
I believe that another stereotype portrayed in the modern day is that women are not expected to talk as much as men, and that men should do all the talking/negotiating because that's the more masculine to do. This is also demonstrated by Kramer (1974) who also said that women typically talk less than their male partners.

Power Concepts - Gordon Brown

The theorist and theory that i'd refer to in a language and power question, particular in relevance to the Gordon Brown speech is Fairclough.

Fairclough (2001)
The power behind the discourse, as stated by Fairclough, is for political influence, particularly in this speech. The speech is generally for the public in informing them of his motives and what he will achieve as Prime Minister. The secondary purpose is to persuade all those who voted for him, that they made the right choice, and to persuade those who haven't that he will not let them down.

Power in discourse- The speech uses specific features which illustrate the power that the Prime Minister has, and to get his point across. The use of personal pronouns such as "we" demonstrates Fairclough's theory of synthetic personalisation which creates the friendly facade the government are trying to pull in collectively addressing the audience, or in this case, the public.
Ideology- The ideology here is the attitude towards the government, which they are trying to improve from the view points of the public. Therefore, they include a patriotic lexical field, accentuating how great Britain are, especially with the new Prime Minister.