If by 'economy 7 boiler' you mean a hot water cylinder fitted with an electric immersion heater, then there is no accurate answer to your question.
The heater contains a thermostat, so will only be using power while the water is below the set temperature.
Overnight, it would typically take 2-3 hours to heat up from completely cold - so even if the timer was working properly, the element would not be on for anything like 7 hours.
If the timer is broken, the element will be going on and off throughout the day as the temperature of the water changes, which will be primarily due to the hot water being used.
The worst case is that you pay for all of the electricity at day rate rather than night rate. With your figures of 45p and 20p, that's a difference of 25p, and if you require a 2 hour heating period every day, it would be about 50p per day.
A 4 hour heating period would be £1 per day.
It's not likely to be more than 4 hours per day, as that would imply you are using the entire contents of the cylinder and then having to switch the heater on in the daytime anyway.