"Of course you tell them there is covid in the household"
Well, not really. When you give the information, you're probably talking to someone that medically trained. And of course, at least some of those folk will be spooked by the mere mention of covid, and they could act to keep you away.
So it's not that you lie. If asked, tell the truth.
But do think about who you are talking to, and also prioritise your own needs.
The practice will have procedures and checklists for receptionists such that patients are adequately triaged. And that will be sufficient to keep people safe. If it doesn't include questions about other family members, then that's because it's a risk that's mitigated by some other mechanism that perhaps you don't know about.
"Just because the government says it’s fine now, it isn’t."
It might not be risk free, but it is a risk that is well-understood, and is mitigated.