I had the same issue with my wife's Peugeot 307. I polished them to perfectly clear, but this only lasted ~1 year.
The original headlights have been coated with UV-resistant clear when they were manufactured, but with time the sun beats this to submission and you are left with just plastic that degrades pretty quickly with ths sun shining on them.
You have three options.
1. Buy new ones, but they are always expensive and takes a lot of time to replace them.
2. Polish them (wet sanding from say from 600 to 5000 grit) and then apply a protective plastic film. See from this person here:
https://www.youtube.com/watch?v=UG54xt56uZo I tried that, but the 307's headlights are somewhat domed and I could never do it without having bubbles underneath and the domed part cannot be done with the plastic film as it does not stretch too well. You may try it with the Berlingo, headlights are pretty flat (not too sure about the 2008 version), so should be doable. That is the easiest way of them all.
3. Wet sand them (600, 1000-1500 grit only). Then spray it with clear coat and wet sand 2,000-4,000 and cutting/polish compound. I did that and it is nearly perfect now. I made a stupid mistake the first time. I wet sanded them 600, 1000, 2000, 3000, 5000 and 7000 grit. They were perfect, better than new. Then sprayed the clear coat, but the clear dries into kind of a spidernet shape or cracks a lot or one can explain it as hairline cracks. I had polished it too good and the clear does not have anything to get hold of, no micro cuts to get inside. Similar to spraying clear coat on a mirror. Sand again and I left it at 1000-1500 and that was pretty good. Of course cutting compound and polishing afterwards. The clear was from a can and I think from paints4u from ebay. Pretty good clear, not 2k, but just the normal 1k. The sanding paper from amazon, some generic A4 sheets, they are pretty cheap. The clear coat lacquer lasts, but you have to be careful not to sand it out. It depends on the thickness of the clear you have put down. I did a few passes of clear coat lacquer, leaving ~15-20min between each coat to harden a fair bit, but that depends on the temperature, the hotter the temp the shorter the interval of clear coat.
If you are interested I can post where I bought all my things.