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It's a sample of N~1700, so +/- 2% for a 95% confidence interval. The responses are weighted so self-selection along socio-demographic variables is mostly accounted for.

Sure, almost all off-the-shelf polling is rather bad these days, but they did their job as well as you can reasonably expect.

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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.

Modern polling is hard because people tend to distrust elites more than in the past. It's a fundamentally unsolvable problem to elicit attitudes from people who lie to you, lie to themselves and make up opinions on the spot.

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.

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