Hello Asbrad,
The filter could be the problem, but before you replace it, try the following first.:-
If the pump has any air trapped inside its impeller chamber it may not start to pump properly. So whenever you want to change the water barrel (say to fill it up), disconnect the pump from the caravan. Then drop the pump into the water then reconnect it to the caravan. This should eliminate any air traps. Now try the pump.
Now back to the filter.
You should not use a filter if its been in the caravan over winter. It may have started to go rather unpleasant. However you may not need to buy a replacement. Caravanners who use UK sites will be pretty certain the water available from the mains taps will be safe. It may smell or taste slightly different but it should be safe. Quite a number of caravanners will fill up a small container for drinks and cooking, rather than using the water from the caravans pipes. Other rely on bottled water.
So do you need a filter in the caravan if all its being used for is hot and cold water for washing? So assuming you have a crystal system Mk1 with a conical filter with a clear cap, then what some caravanners do is to unclip the filter cartridge from the clear cap and simply refit the clear cap, using a little vegetable /cooking oil to lubricate the o ring seal. Be careful not to over tighten the cap as this can split the crystals housing.
Hope this helps.