Washing machines use anything between 1.2kW and 3kW of power. With electricity costing roughly 20p per kWh, that means that the cost of running a washing machine for one hour is theoretically in between 24p and 60p. Taking that up to 1h 45m pushes the figures up to between 42p and 105p.
However even the most powerful of machines won't be using full power all of the time, as the water will only being heated for part of the time. So the cost of your wash might only be in the range of, say, about 35p up to about 80p, with perhaps 60p providing a single ball park figure.