I've got a Brother MFC-620CN Fax (plain paper), answering machine, scanner, photocopier, printer (cost about $350 NZ & the NZ dollar is still about 1/2 the value of the £ I believe) with a socket to plug my cordless phone into. It works great & the whole thing sits neatly on my desk. I love it & I regularly use all of it's functions, although the fax function is perhaps not as often needed as the others. I've had it about 2years now & never had any trouble with it.
The reciever mic of the inbuilt speakerphone has a low pick-up range & you have to stand very close to the machine to be heard. but It did a perfectly good job of recording my answerphone message & I never actually use it as a speakerphone so that suited me just fine.
I bought it when I was setting up my info research business at home. Space is limited so I wanted something multifunctional & compact. The business didn't come to anything unfortunately (the breaking the back thing makes it hard for me to stay sitting or standing for long... bit of a bummer when you're setting up a computer research business... but i ain't given up hope yet) But I've never regretted getting it & it's seen some pretty hard useage.
Interestingly it is sold (here anyway) not with the multifunction printer-scanners-etc... but with the fax machines, & is a fraction of the cost of the printers even though it does more than most of the printers do.
I expect that there's newer models out there now, 2 years is a long time in the world of technology, but it still might be worth checking.