It's more likely that on quiet nights/days it's simply not cost effective to open. During a weekday a small pub might literally have one or two customers. They're traditionally owner-operated for a reason, and the reason is because the margins don't allow for staff.
Definitely changing that though, esp over last 10 years. Many pubs in London (and increasingly other areas) will put an "optional" 12.5% for service for food, especially if they have a "dining area" off the main bar. It's also increasingly common for pubs to have people asking if you'd like another drink, and charging you 12.5% for the pleasure - this seems to be a lingering effect after covid where you couldn't go to the bar to order.
At least when food comes into it they may do, quite a lot of tips where my brother worked a few years back (pooled and shared between bar & kitchen staff). Nothing like the US though indeed.
Barstaff don't get tips in the UK
It's more likely that on quiet nights/days it's simply not cost effective to open. During a weekday a small pub might literally have one or two customers. They're traditionally owner-operated for a reason, and the reason is because the margins don't allow for staff.