We have a Franke triflow tap in the kitchen. Cold and hot are both
softened water.

Drinking water is via a Triflow Hiflow filter which is due to be
changed. It is the plastic one on the left on this link

http://www.the-sink-shop.com/waterfi..._identify.shtm

Inlet goes into the main body at the top. Outlet is taken from centre
top after water has been through cylindrical filter.

We want a fairly good flow and a filter is likely to cost around £22 + P&P.

Water around here is pretty good with no lead or off tastes. In the
circumstances I don't really want to put in a new filter. Can I just
leave the filter out of the casing or is there a risk of some water
becoming static at the bottom and nasty things breeding? The water will
be at mains pressure with nothing removed.

Alternatively anyone know what adaptor I would need to connect the inlet
and outlet pipes of the filter together? They are different sizes and
disappear through holes in the back of the fitted kitchen unit making
re-plumbing difficult without trashing the back of the unit.

TIA for all replies not involving angle grinders.