I am changing my internet service provider

because the present company has advised me that they cannot provide me with the service I require.
All I want is a plain vanilla sort of service. I want to be able to download documents, upload documents, write the blog, do a little searching, "talk" to some friends via social media - AND use my email.
Since I was required to move to the NBN (National Broadband Network) I have experienced frequent (many times a day) drop outs. I have had to "reconnect" constantly. No, there is nothing wrong with my devices. It is simply that too many people are trying to use too small a bandwidth. 
Apparently it is a common problem. Companies, in an attempt to make an acceptable level of profit, are simply "not buying enough to supply enough". It is likely that the system itself will eventually not be able to supply what people need - even if companies are prepared to pay for it.
I don't watch movies or play games on my computer so I shouldn't need the "super fast" speeds being promised. I just want something reliable that won't drop out.
So I spent some time on the phone yesterday. The new company assures me it can provide me with something that "should be better than that" of my old service. I certainly hope so.
But, it leaves me with a major problem. I still need an email server. I would also - for about 600 plus reasons - like to retain my old email address. Today I have to tackle the old company about that. I am not looking forward to doing it. Our relationship is a little tense. I am leaving them - that it is at their suggestion not mine makes no difference.
I really don't have the time to email so many people, organisations, websites and more and tell them "Please change my address in your records". I know some people won't do that anyway and that when they want me they won't be able to find me. For most people that might be irritating and disappointing but in this case it could be life-threatening. Doctors in particular are busy people. They don't need to be bothered by that sort of thing. I can do the "BCC" trick for some people and send out group emails but I can't do it for everyone. 
But, if they don't let me keep the old address, then please bear with me as I work out a way to get a new one and tell everyone. Lives may depend on it.