sealed hot water boiler

i have a Worcester 9.24 electonic central heating/hot water boiler,the problem is unless the hot water tap in the sink is run very slowly the water will not get hot,and when it does if you turn the tap up it gets cold,the bath water upstairs does not get hot unless the central heating is on,this is supposed to supply hot water on demand,when you turn the hot tap on the boiler fires up but as described doesnt heat the water,we have had the plumber out but all he says is the water pressure in the taps is to much for the boiler,now this boiler used to supply hot water on demand,so am i right in thinking the boiler is misfiring(ie knackered),and is the plumber blagging so as not to give us a new one,my landlord are the local authority,he stated that there needs to be 3 things wrong with the boiler before they replace it,,,,,just off now to clean up after my grandaughters rocking horse,any assistance would be greatly appreciated