I'd expect a lot of interference to be emitted from the 'Homeplugs' system, but it may be your only option.
Cat 5, and Cat 6 cables are a lot more carefully engineered than they look. They're "twisted-pair" systems, which is a way of reducing interference. The idea has been around since the dawn of audio communications, analogue and digital, but these are high-tech versions, and the transceivers (the electronics at each end) are very picky about the quality of cable they're connected to.
The only good thing is that all modern digital systems of this type are designed to 'degrade gracefully', so that, when there is interference or a cheap cable is used, the data rate will usually slow up to something the cable can manage, rather than fail entirely.
@Harbo:
It's most likely to be just a poor IDC ("punch down") connection on the back of the wall box faceplate though, and the ISP's engineer couldn't be bothered to check/remake it.
Assuming there's a few inches of slack cable at each end, it's an easy matter to re-make the connections - the punch-down tool is pennies from eBay or Maplins, etc., and the plates and wires have unambiguous colour coding.
Even if it is damaged, it might still be salvageable: Cat5 or Cat6 has four twisted-pair circuits, but Ethernet (computer-to-computer) connections usually use only two pairs at a time, leaving two pairs unused (two Ethernet connections can't share a cable, because of interference).
It may be that you have enough undamaged pairs to make your 'faulty' cable work for you, but you'd have to check them out individually. As long as you keep to the designated 'pairs' (solid green with green-white, solid orange with orange-white, and so on), and don't mix different colours together, you only need two sets to work properly and it's probably fine*. I can't remember which two are usually used, but Google will find it quickly.
Cheers, E.
*purists will argue about that for ultra-high-speed connections, but at typical broadband speeds it probably doesn't matter a bit. Not using proper cable matters loads, though.