To some extent, it depends on your subject. In my subject area, a masters is now usually required at a high merit or distinction level to progress to a PhD. However, I do know people who have successfully gone straight from undergrad to PhD, with 1st or good 2.1.
If you're willing to self-fund, and you have a 1st, you should be able to get into a very good university.
Talk to potential supervisors, and they will offer opinion on whether you need research experience.