'overflow-x: scroll' inside a fixed div prevents vertical scrolling on ios

The below css fixes your issue

html,body{height:100%}
body{background:red}
p {
  font-size:22px;
}

.item {
  display:inline-block;
  width:80px;
    height:60px;
  font-size:78px;
}

.scrollable {
  width:350px;
  white-space: nowrap;
  overflow-x:scroll;
  overflow-y:hidde;
  position: relative;
  -webkit-transform: translateZ(0);
}

.pop-up {
  position:fixed;
  height:300px;
  background:blue;
  border: 1px solid #000;
  width:100%;
  top:0;
  overflow-y:scroll;
  z-index:9999;
  -webkit-overflow-scrolling: touch;
}

.somemoretext {
  padding-top:600px;
}

The lines containing -webkit- are the key to make the scrolling work in Safari.
In the .pop-up DIV you need overflow-y: scroll and –webkit-overflow-scrolling: touch to force the scrolling. In .scrollableyou need –webkit-transform: tranzlateZ(0); to move the actual html content up and down, other wise the DIV will scroll but the overflowing content will NOT show.