One in five reported rapes in London leads to a caution or charge.
Men should make certain that a woman has consented to sex to avoid being accused of rape, a new campaign launched by the Home Office is to warn.
The magazine and radio adverts and posters are aimed at reducing the number of sex assaults taking place when a woman is very drunk.
It comes amid low conviction rates for rape cases in England and Wales.
A law change has been mooted allowing juries to decide whether a woman was too drunk to give consent.
Mike O'Brien, the solicitor general, told BBC Radio 4's File on 4 the law "may need some clarification" to allow a jury to decide whether the woman was too drunk to be capable of consenting, and whether she did consent.
Mr O'Brien said if the law were to be redrafted, he expected the number of rape convictions to increase.
A recent study by the Metropolitan Police revealed that more than a third of women who reported being raped had consumed alcohol immediately before the alleged attack.
The Home Office campaign - costing almost ?500,000 - will begin on 14 March with radio adverts, followed a week later by include adverts in men's magazines, stickers on condom machines and posters in pub toilets.
A Home Office spokeswoman said the issue of consent was central to the Sexual Offences Act 2003, which stated that a person must agree to sex by choice and that must have the freedom and capacity to make that choice.
"Giving consent is active not passive, and it's up to everyone to make sure that their partner agrees to sexual activity," she said.
Amnesty International UK said the campaign was a "step forward" but that it must form part of a wider plan to tackle low conviction rates and "a sexist blame culture".
"The results of an opinion poll we commissioned last year showed that a disturbingly large proportion of the public blame women themselves for being raped," director Kate Allen said.
"In the end, a truly comprehensive approach can only come through the government backing an integrated strategy to end all types of violence against women in Britain."
BBC Home Affairs Correspondent Danny Shaw said the aim of the campaign was "to stop young men taking advantage of drunken women and having sex with them".
He said many cases failed to reach the courts because victim could not remember all the details due to having been drunk.
And in some circumstances judges have stopped trials because it has become clear that the woman was very inebriated at the time of the alleged attack.
One woman told File on 4 she was raped by a man she knew after sharing a taxi back to her flat after a party.
She said the man invited himself in, she remembers sitting down on the sofa, having had a lot to drink, and the next thing she knew he was raping her.
The case went to trial but the man was acquitted on the orders of the judge, who said her evidence was "unreliable" because she could not recall details of the alleged attack.
She said: "I wanted to absolutely tell the truth so if there was anything I was in any doubt about I would say, 'Well, I'm not sure,' or, 'I can't remember'.
"And the judge stopped me and said, 'So, it's possible you were actually making advances to the defendant during this period?' and I said 'All I've told you is from the moment of sitting on the couch to the moment of waking up I don't remember anything.'"