It strikes me as somewhat odd that the British market doesn't have the same basic phone models we have in the US, but these
mostly have the same functionality as the one I have in the US. Multiple handsets, plus the base has the ability to Bluetooth to two cell phones. I have a larger home, and we have the five-handset version (the feature is Link2Cell in the US version if you want to check out Amazon's offerings on this side of the pond for comparison). You can leave your cell phone plugged in and charging near the base, but you can still make and receive calls on it (in addition to on a landline, should you still have one - I do, although it's VOIP). I believe the newer ones are able to notify you if you get a text - though not able to read it remotely, which would seem to be a likely feature for the near future.
FAX machines are covered under a different standard, T.38
, which just has to be implemented at your VOIP adapter/ATA. The Obihai 200 and 202 both support it, and they're not exactly expensive. If you have a modern hybrid service, where the telephone adapter appears to be analog to you but is VOIP from the internet provider's box upstream, it should already be doing this for you.