Op. So, you haven't wanted the 'romance-y' aspects of a relationship or a wedding thus far, but some part of you is a bit sad that you might look back and feel you made something romantic a bit... Formal and dull? (formalising your relationship on a forever basis - it's pretty romantic, in the real sense of the word. I personally don't believe doves or roses or whatever to be romantic, but stating your intention to be together forever in a formal way IS pretty lovely).
You're allowed to change your mind you know, or have a feeling which is new or different from those you had before. Just because you hadn't wanted it before and now you do, doesn't mean you can't feel differently, and all the people saying hard cheese, you opted out of romance so no ring for you are being a bit... Well, mean! Isn't marriage or long term partnership about growing and changing with a person? It's not like you've gone completely mad and started demanding a massive wedding in Westminster Abbey :)
It's a small gesture, an indication of your intentions, and a little tiny bit of glitter added to a legal ceremony. You're not asking him to spend a fortune, the money is joint, you just feel like you'd like it. There's nothing wrong with that. Talk to your DP - just explain that you feel this way, that you're not pressuring him, but would an afternoon bumbling around Hatton Garden be fun, have some lunch in a nice pub, just spend an afternoon together and pick up a sparkle for your finger? Maybe even go with a girlfriend in advance and narrow it down to a couple, then take him, let him get it, pop it on your finger then go have a pint in a sunny beer garden. Doesn't have to be ostentatious. But it's something that clearly means something to you, whatever the reason. However it started, it's become a societal thing, and fgs, it's nice so who cares if it was a deBeers campaign? I loved having my engagement ring in the run up to our wedding. Every time I saw it it reminded me, a little 'ooh' and a smile to myself. I didn't need it, it isn't a big flashy ring, but it meant something to me. DH went and designed it and had it made for me without my knowing. We'd talked about getting married and my DH is not romantic at all - we don't do valentines, don't really celebrate our anniversaries (not in a big way and I can't tell you the date we 'got engaged' on the sofa in our slobs one Sunday afternoon - but I was very touched that he'd done something which he just knew would make me happy.
Maybe it just feels weird asking him to go because it means admitting you want it, even though so far you haven't? You don't want him to feel you've suddenly got different ideas? You said if you asked him, he'd probably go without fuss: is it that you wish he just knew you'd changed your mind? If its that, don't expect him to be a mind reader, just 'fess up. You love him, he loves you, you've got kids. Trust him with your feelings then hoick him into a jewellers and take him for a pint after. Gethin something too perhaps? I have a friend whose fiancée got him an 'engagement' iPod :D