Expose them to some of the things that are involved in the running of their country. Many of them are free.
Take them to Parliament. You can email your MP who will get you in, for a tour and to watch a session. But it's popular, so if you want to do it out of term time you may have a wait of many months. Do your DC know who their MP is, and what s/he can help with, regardless of their personal political allegiance?
Take them to Court. Over 14s are allowed in the Public Gallery. Your local Magistrates' Court would be a good start, but I really recommend a visit to the Old Bailey (there are two buildings, the old one is more atmospheric). Mobile phones are absolutely forbidden, so leave them behind or trust a local shop to hold them for a fee. When I've taken DCs, I found the officials really helpful at recommending which court had the interesting case.
If in London, wander round the Inns of Court. Fascinating and historic. Also the Temple Church - it's small but they offer tours for a few pounds.
Take them to a service or two in a cathedral. A High Mass and something more relaxed. Maybe a contrast between Roman Catholic and Protestant. Let them see what goes on and appreciate the high quality music. Also a service in a local church. A mosque, and a Hindu temple (eg the amazing one in Neasden, London). I don't know enough about them to know if anyone can turn up to a 'service' or if it would be more appropriate to arrange a visit. (See, a gap in my life education.)
Make sure they are familiar with the library and borrowing books. Also the concept of the reference library, generally in larger towns, where you can consult all sorts of tomes, maps and local history. Do they know their County Town and its significance? Which are towns and which are cities?
Familiarise them with art galleries and museums, local and the big London ones. Also theatre, ballet and age-appropriate opera. The ENO at London's Coliseum is free for under 21s, performs in English and has the words up on a screen above the stage so it's easy to follow. They don't just do 'heavy' opera; they've just had a wonderfully silly and funny Iolanthe (Gilbert and Sullivan - political satire brought up to date). They also have 'relaxed' performances with the house lights slightly lit, wandering in and out not frowned upon, and a room to go and sit in if escape is needed.
All these things, and there must be loads more, are things that people can feel 'aren't for them'. But they are. They are for all of us. Religious services can be used to mark events that might be relevant at some point. Just about anyone can get called up for Jury Service. We could be summoned to the Magistrate's Court, or threatened with it. It's good to know what these things are really like not just something scary and incomprehensible that other people understand. It's our children's country; they should feel at home in all aspects of it.