You may find your new TV has a lower tolerance to interference, and your new Samsung TV will not channels with poor\low signal. Freeview have a list of suggestions which can be found here.
To start with I would perform a factory reset of the TV to clear all settings, check the coax cable is undamaged and connected firmly into the TV and wall, then re-tune.
If the channels still do not reappear, I would consider investigating the signal strength (which may impacted by a poor coax cable, poor quality aerial or incorrectly installed aerial).
Looking at how the 3 channels you are watching are broadcast More4 and Film4 are part of the same group as ITV and Channel4, so would tune into ITV2 for example, then look at the TV's signal strength, as see if adjusting the aerial improves this, before then doing a further re-tune.
You can access the channels signal strength by selecting the channels, pressing the "D.Menu" button on the remote, selecting "Setup", then "System" followed by "Signal Information" from the on screen displays. You may then wish to compare this to another channel such as BBC.
Should you need anything clarified please let me know.