>>211584114 (OP)not even 28days
The film opens with the genesis of the rage virus. Precisely 28 days later, Jim wakes up to a different world. He meets Mark and Selena who take him back home the next day. Mark is then killed that evening, and Jim and Selena seek shelter at Frank and Hannah's apartment. Frank says that the trip to the blockade could take about 2-3 days. The trip takes roughly 2. Frank is killed, and the soldiers take in Jim, Selena and Hannah. We're right around 31-32 days after the initial outbreak.
Major West tells Jim "8 days ago I found Jones with a gun in his mouth. He said he was going to kill himself because there is no future." This of course is when it is revealed the soldiers' broadcast is all about luring women.
Let's say there's 32 days since the initial infection at this point. Obviously the infection did not take out England in one whole day since there had to be enough time for people to put up the pictures/letters in the public square and for newspapers to announce an evacuation. So, even if that all occurred within one day (and it's far more feasible that it occurred over a couple), that still leaves about 2-3 weeks between the infection actually doing major damage to England and Jones' attempt at suicide.
This means only three weeks passed before the soldiers turned rapist. It took about 16 days (give or take) for them broadcast a lure for women to rape.