Yes the logic is just utterly screwed. You can't mix with another household in your own home, but you can unintentionally mix with many other households in the local pub. If I lived in Greater Manchester, I wouldn't really know what to do as these rules don't sound like they would work at all in terms of controlling the spike.
I'm not saying it's targeted at Eid, but it looks like it is targeted at Eid.
The grim takeaway for me is, I don't think this virus can be controlled at all unless we have a prolonged period of full lockdown, perhaps 6 months or more, no international travel etc. Personally, I don't think I could do that, working full time, disabled wife, child to look after too.