I am at the beginning of setting up a UK business and started it with one share valued at £1.00. I am the owner of this single share. I am now wanting to pay the amount I owe for the share to the business, since I didn't pay any money for it at the time I "bought" it (the business is set up as dormant for now). So how should I pay for my share? Should I deposit the money into the company's business account?
A limited liability company's shares have a nominal value, sometimes called "par" or "face" value. This represents the extent of the liability of the shareholders to the creditors of the company in case the company goes bankrupt - hence "limited liability".
Once the shareholders pay the money to the company, the shares are "paid up" and they have no further liability to creditors. So you should keep track that you've done it.
In principle you could perhaps be keeping the business money in a personal bank account, in which case paying up the share capital might just involve updating your records and not actually transferring any money. But that sounds like a recipe for confusion further down the line and I'm not sure if there are any other gotchas.
The nominal value is independent of the "real" market value of the shares. Suppose that your company has two shares, each with a nominal value of £1 that you pay in, and it then goes on to make £98 profit. Each share is then worth £50 even though they have a nominal value of £1. If you sell one of them to someone else, they should pay £50, and that would go to you, not the company. If the shares weren't paid up then they should pay you £49 and would owe the company the remaining £1, but I expect most people do pay up their shares before they split ownership as otherwise tracking them is very complicated. Normally the share capital is very small.