Polling has un-earned respect lately in the US. Is there any reason to suspect opinion polls are more reliable in the UK? Afaik people are just as shifted away from landlines there.
That said, modern polling uses a host of techniques and is of course not tied to landlines. Companies use access panels of available participants, f2f sampling (walking to random people's houses, but that's expensive of course), and in particular statistics such as poststratification.