Well yeah - if they're letting people into their home who don't live there, or if people they live with are breaking rules, or are in a high-risk job. They're catching it from people, not the four walls around them!
What makes you say that people who catch it at home are getting it from people who shouldn't be there? In the large majority of cases, people who catch it at home will be getting it from other family members.
I feel I need to point out yet again that in Wuhan/China (the only place that had a bad outbreak and then managed to massively suppress/nearly eliminate the virus), it was centralized quarantine that did the heavy lifting, more than lockdown. The Wuhan authorities looked at the data, realized that most of the infection was caused by the virus swirling around people's dwellings with family members infecting each other at home, and started quarantining infected people in hotels.
I've discussed this point on Mumsnet a couple of times, and it's been fairly clear that there is very very little support for centralized quarantine in the UK.
If that's the case, then I will tell you right now that no amount of lockdown, "being strict" and "following the rules" is going to suppress this virus to really low levels, let alone eliminate it. You need centralized quarantine as well as lockdown if you are actually going to be serious about suppressing the virus.
If centralized quarantine is not politically possible for the UK, then the best situation for the UK right now is to concentrate on pumping the vaccine out REALLY fast, keep borders tight to avoid any new variants being brought in, try to beat down viral loads as hard as possible (can't quite understand why there is so little emphasis on ventilation in the UK....), and accept that there are going to be quite a lot of deaths among the elderly.
That's grim but I can't really think of any alternative. The UK can't really afford to do lockdown much longer, and lockdown alone (without centralized quarantine) is never going to suppress the virus, just lower the levels a bit.