The simple answer is yes, but I wonder why?
It may help to understand that the filter system you have does not purify water, it mainly prevents small particles from getting through, and it can reduce some problems of taste or smell with poor quality water, but its no where as effective as a table top filter jug.
In fact there is a consensus that if you are only caravanning in the UK there is no real need for an inline water filter at all. Many caravanners remove the clear plastic cap from the cartridge and just fit that to keep the system sealed and functional but without the filter.
If you have any doubt about the safety of water for drinking, it is safer to have bottled water.
I suggest simply making the top blue pipe connection to the end of the filter housing, and when the filter is expired (normally 30 days usage) and then just use the clear plastic end cap to seal the system.
If you do decide to filter all the water, you will need to join both blue pipes to the upper connection, but you will also have to ensure the lower connectio is fully closed off, otherwise you will flood the area when the pump runs.