Yes, all the electricity you generate is free and can be used to run your household appliances from lights to the dishwasher, a hairdryer to a heat pump! A typical 4kW domestic array with a southerly unshaded aspect in the north of England will generate around 3,500kWh of free electricity every year. The average UK home consumes around 4,000 to 4,500kWh of electricity so a PV array can make a significant contribution towards this.
It of course must be remembered that peak times for electricity consumption are the evening and winter months when the sun is not shining and the panels may not be generating as much electricity.
Any electricity you do not use can be sold back to your chosen electricity company through the Smart Export Guarantee though this will not be as financially beneficial as if you use your self-generated free electricity. Small changes in routine such as using the dishwasher during the day rather than overnight will maximise the benefit of installing a solar PV system.