Normally, movie producers would obtain permits to shut down roads around city filming locations. However, this is not usually permitted in London (even huge productions like Bond get very limited privileges in London), unlike a lot of America cities. Although, it seems that the producers were able to get some road closures, but under very limited conditions.
To get around this, the empty London scenes were shot very early in the morning - sunrise in London is about 5am in the summer, and there is a long dusk before true sunrise which gives a decent amount of light. In fact, the dusk light (the golden light you see in some of the stills you posted) was probably used to provide an additional sense of eeriness to some scenes, along with some filtering/grading to reduce its effect in others.
Before we started the main shoot we took a week in July, beginning each day at three or four every morning and would wait for the sun to come up
We were able to shoot for an hour or so before the city got too busy for us to hold back the traffic. It was very exciting, and when you see the whole of Westminster Bridge and the embankment all closed for you, and the traffic stopped, and you can't hear anything, it was thrilling but strange as well.
Source: 28 Days Later : About The Shoot
A lot of the scenes are filmed in the inner cities of Westminster and London (the City of London itself is a square mile in the middle of Greater London), and these are mostly commercial and government offices - not a lot of residential areas - so there was not a huge number of people waking up and heading to work.
However, even in the wee hours of the morning, Westminster and London and the surrounding areas are not completely empty. I think if you look carefully there is at least one brief shot of a moving bus in the distance. Mostly, the crew would reset and try for another shot if something like that happened.
I remember reading around the time of the movie coming out, that a bigger problem were drunken revellers spilling out of nearby bars and clubs - the production crew hired a number of attractive young women to distract and guide people around the shoot.