"let me inform" is a correct and usable phrase in written English.
You can use it when you want to introduce a piece of information that you will share with someone. For example, "Let me inform you that I have been accepted to college."
Retrospectively, let me inform you that not much happened.
"Then let me inform you, Deirdre, that at this point I have replaced all but a couple of the six or seven stones necessary to give the souls their deserved respect.
If we are to attribute the suppression of female autonomy as a upholding of fundamentalist Christian values, let me inform or remind you that abortion is not mentioned in the Bible.
But, er, in case you're even thinking about going elsewhere for an hour, let me inform you that England are beating Wales by a goal to nil and George Osbourne is still messing up the economy.
But since you insist on an explanation, let me inform you that you were seen at a so-called 'literary salon' in Shkodër, one of those rat holes for the town's aging Catholic bourgeoisie who yearn to turn back the clock".
Let me inform you of the steps Duke is taking to respond to the recommendations of these reports.
"You didn't let me down," he quietly informed Jody Latham while sacking the Shameless actor on day seven, "You let yourself down".
She rings to let me know and also informs the agency that I will need a substitute, but the agency does not contact me and more often than not, no replacement arrives.
Since I have already established that I am not a social theorist nor very well informed, let me share this theory I have about society and why there is less interest in female sports.
Let me take the liberty of informing these people that they are just as bigoted and just as responsible for the actions of this administration as those who voted it in.
Yet this investigation provides a crucial opportunity to listen to students and let them inform the debate on education reform.
