I have monitored my usage very carefully over recent years and submit readings every 4-6 weeks so i don't have to rely on estimated bills, but whenever I missed a reading and received an estimated bill I found it spookily accurate. I understand they have sophisticated models which give a very good estimate based on known usage patterns at different times of the year and reflecting actual weather conditions, so I doubt they do manipulate estimates in this way- but of course they will be over or under for some individuals but right on average.
When there is a rate change it's best to submit a reading as close as possible to the date of the change, and I've found that if I read the meter when it's dark it's quite possible to transpose two digits and thereby overstate the reading at the date of the change