The purpose of the filter is to split the ADSL and phone signals, preventing the ADSL signal causing noise on the phone, and preventing the phone from sucking out the ADSL signal - if you plug an unfiltered phone in, it effectively shorts out the ADSL frequencies.
Simple solution, if you have a 99p store nearby, they may have ADSL filters (mine does), just pop a filter on the phone and it should work fine - actually, you want your best quality filter on the phone, and maybe use the cheapo on the modem, as if the filter is of less than ideal quality, it will be less of an issue if only used as a connector (the ADSL side just connects straight through, only the phone side is filtered).
http://www.adslnation.co.uk/support/filters.php