I'll stay out of the washing machine conversation as Nigel is a lot more clued up than me.  Regarding the water supply problem, how have you measured your pressure at 1.5 bar ?  Is that at the mains supply to the house or at the input to the boiler ?
A couple of other things that have occurred to me.  You said that taking the filter off the tap improved the flow rate.  Not wanting to teach you to suck eggs but have you tried taking the rose off the shower head?  If you can fill a 10 litre bucket in about a minute with it off then your flow rate is OK so soak the rose in vinegar for about an hour to de-scale it.  You may also find very small stones blocking the holes in the rose.
The other thing is to check that your boiler is of sufficient capacity.  Usually expressed in Litres/minute which indicates how much water at 65 deg C it's capable of producing in a minute.  Anything less than about 10 is only really any good for a single point hand wash.