This may be a long shot, but does anyone know of a mobile phone, which works like a cordless home phone?

By that, I mean it has a charging base station which, if possible, contains an answering machine.

All mobiles have an answering machine, it's just called voicemail.

Pretty much every phone. You just buy the phone, the answer phone is built in, then you just buy the official charging dock.

I know about voicemail.

I was looking for something like a normal answerphone, so I would've have to keep dialling in to hear my messages.

Well then you need an iPhone on EE, Orange or O2 with Visual Voicemail. Oh, and a charging dock which Apple will flease you for

Or... an Android phone and Hullomail on it (works on iPhone to).

These are systems that download the voicemail to the handset and you play them by tapping the message on the screen.