A couple of months ago the new "visitors platform" opened for the Gorham's Cave site in Gibraltar. I couldn't find much information online, so just assumed it was a publicly accessible area, wth a few signs, like most lookout points. However, that's not quite the case in Gibraltar...

Firstly, upon arriving at the entry, there's a sign stating it's only open 10am to 2pm, Monday to Friday. Luckily it was late morning on a weekday when we visited, but it would be a pity if you travelled all the way here on a weekend, to find it wasn't open. Secondly, there's an entry fee charged. If you're also visiting the museum (which we didn't quite have time to include), it's 8 pounds, otherwise it's 5 pounds. Luckily, they take credit card for if you don't have any pounds on you. The lady at the counter said that the entry fee covered the signs along the platform (about 3 or 4) plus a "presentation", which I assumed was a video presentation.

We firstly looked at the signs and peered off to the cave entrances, visible just above the water line. Luckily the rain virtually stopped, improving the visibility (initially we couldn't see the top of the Rock, let alone Africa). We then let the lady know we were ready for the presentation. We ended up being very impressed that it was a personal talk by one of the very knowledgeable museum staff members. He gave us plenty of information, and was fine with answering all our extra questions. (An interesting tidbit: Neanderthals are named after the Neander valley in Germany, near Düsseldorf, but there's no chance of the site being made a WHS, as no-one quite knows where it was, let along the site having being preserved.)

If you have better weather than we did, I would recommend doing the Mediterranean Steps walk. It runs along the steep slope just below the top of the Rock, within the WHS, and visits some other caves higher up the Rock, that also show evidence of prehistoric inhabitation. 

One last recommendation: there are about 5 parking spaces at the visitors platform, only 1 of which was used on the day we visited (probably by a staff member). And they're free! Rather than leave you car outside Gibraltar like we did (and pay for the #10 bus from the border, then pay for another bus to Europa Point, then walk along the side of the road from Europa Point for nearly 1km, and then pay for your parking when you return to it), just drive here along the eastern side of the Rock. If no spaces are free, there's more parking at Europa Point.