Thailand forum

you can go down to Kradan on the fast Trang island daytrip boats which leave Lanta around 8am. I used this method a few years ago - the cost was 400baht and it took maybe 4 hours, but this included a stop for snorkeling the islets between Ko Ngai and Ko Muk plus a swim into the incomparable Emerald Cave on Muk. Note you aren’t guaranteed these extras - the order of the schedule varies according to the tides - it's hard to swim into the Emerald Cave at high tide on some days of the month.
Any resort or travel agent on Lanta can arrange this trip for you. Note it runs back to Lanta in the afternoon, but there is no service in low season - roughly May to end of Oct.

Now the problem from Phi Phi is that the first ferry to Lanta will get in after the Trang Island daytrip boat leaves - so you will have to spend a day on Lanta which is no hardship - better than blowing most of the day getting to Pak Meng and having to overnight or charter an expensive longtail. Note the National Park guys on the pier at Pak Meng will most likely charge you a 200baht park entrance fee too.

I just had a look at that link - I'm thinking that's the Trang Island daytrip boat they're talking about.
Maybe Royal Fern Co run it - or maybe the website is a bit sloppy and should have taken a new paragraph when starting to talk about the boat to Ngai/Kradan.