Upvote:6
What happened to you with your current passport happened to you and will stay with you also with a new passport.
But as you should renew your passport soon, it does not hurt to do it a bit early. You will then no longer have the big X in your passport. But when asked about whether you have been denied, you have to answer yes. If you answer no and they find out you will be in bigger trouble like a long time ban and the need to apply for visa in more countries.
The UK will be able to connect you to both your new and old passports.
As you have noticed other countries may ignore the denial, but do mention it when asked about it.