I'm afraid I cant see that laptop so it's a little hard to give a precise answer.
Laptops on the mains use between about 15 - 75 watts depending on a lot of factors such as screen size, processor, load, screen brightness and so on.
if it's a really high power laptop (75 watts) and assuming your electricity cost 15p a unit (which is pretty high) it would cost 27p to run for 24 hours
If it's a really low power laptop (15watts) and with the same electricity costs it would cost about 6p for 24 hours.
The difference between running on mains all the time and running on batteries and then charging is going to be so tiny it's not worth worrying about.