Franking machines can be topped up online* 24 hours a day, 7 days a week and it only takes a minute. Even when the post office is shut you will never run out of postage.
Also processing out-going mail becomes less of an odious task. Mail items can be easily weighed and correct postage applied. Batches of letters can be quickly passed through the franking machine and on their way.
In the last two years, the Royal Mail has dramatically increased the discounts on franked mail. Clearly, for the Royal Mail, handling franked items is a lot cheaper than issuing stamps and processing stamped mail, so it makes sense for them to encourage businesses to frank their mail.