Before booking, make sure to choose your preferences in your 1865 member profile page of which airline you want to earn the mileage on.
So if you want to earn UA miles, then choose UA and key in your FFP number. Afterwhich you will book the hotel and once the stay is completed, the miles will be transferred to UA in due time. If you want to earn on SQ or CX, then do the same thing. You do not have to present the FFP card, you just need to make sure you choose the FFP before booking the hotel.
Here's the
main Langham 1865 thread.