Where can I do this with a reputable agency ion Phuket ?

I guess that any travel agent can fix you up with train tickets even though the nearest train station is way over in Surat Thani.

Booking on line ---> http://www.thailandtrainticket.com/

It used to be possible to book tickets through thairailticket.com which is operated by State Railways of Thailand, but this service was suspended. You can also try to call Surat Thani Railway station but only on the day you want to travel, 077311213, but my experiences with this are hit and miss.

Seat 61 website has links to 3 agents that can do .. 200 fee extra per tix

1st class get booked out almost immediately so hard to get unless your close to 2 months prior