E mail everywhere

Hi - This might seem like a really stupid question but here goes. We have a range of lap tops and tablets at home, some windows, some android and some apple. Over the years I have tended to use whatever browser is on the machine to log into my btinternet.com e-mail address. The problem I have is that I have e-mails filed and saved all over the place which makes finding anything a bit of a problem. Is there an application etc where I could consolidate them all in one place which would then allow me to log on wherever I am and see all my saved messages?
Sorry if this sounds a bit dense.

E mail everywhere