The general rule out here in Canada is that when you're wearing your uniform you ARE on duty. You're allowed to wear it to and from your place of work, but apart from that you need permission from your CO. That being said, everyone who goes out for a drink after work usually stays in uniform until they actually get home. But there are plenty of Legion Halls and such in my city that are more than happy to see service men and women.
The thing about being officially ON DUTY any time you're in uniform, on bass, or on DND property (including vehicles), is that anything you do wrong puts you under the Military Codes of Service Discipline. Get drunk and disorderly in uniform, and you're looking at a military punishment on top of whatever you get civilly.
I think that the ON DUTY component of wearing the uniform does encourage members to be more responsible while in uniform in public. We tend to look after each other.
Granted, in Canada we're very rarely considered targets for violence, so I can understand the additional concern that you have in the UK. Biggest problem out here is that people mistake an airmen in blues for a bus-driver, and a naval officer in whites for a pilot at the airport. Hell, even in my blues I can't even count how many times old ladies have come up to me at the airport and asked me what time their plane departs.
Myself: "Well, you'll have to check the departure's sign, ma'am. I don't work here."
Old Lady: "But you look like you work here."
Thinking to myself: "'Are you the old lady that the nice folks from the Home have been paging on the PA?' No no... Can't say that... um..."
Myself: "Perhaps this gentleman can help you out!" (at which point I gesture towards the nearest naval officer and quickly exit stage left)
In any case. A lot of that junk in Canada has to do with an the public's under familiarity with the Canadian Forces. Out here we could certainly use a more visible presentation of military personnel.
All of that being said, being "encouraged to wear the uniform in public" means to me that people should be more willing to wear their uniform to and from work each day, even if they have to make a few stops on the way. It increases visibility, and a steady diet of such things for the public may help to increase acceptance and familiarity. How long does it take the average person to get home from work? 30 minutes? We're not talking about flirting with disaster here, we're talking about maybe an hour ouf of an entire day.
I certainly don't think that they mean to suggest that a servicemen puts on his uniform in the morning of his day off and goes out to cut the lawn, visit the market, and catch a film at the nearest cinema. That would certainly be asking for a kickin' eventually, and it would make you look like a bit of a tool in my opinion.
Besides, if you don't have to change into the uniform AFTER you get to work and BEFORE you leave, that gives you more time in the morning for things like breakfast... or 5 minutes sleep... or even just 5 minutes of zen. lol Do what you will folks.