Every share has a nominal (or par) value. It may be a £1 share or a 10p share, or whatever. The nominal value is usually expressed in sterling, but can be in any currency.
A company may not issue any share at a discount, i.e. may not sell it for less than its nominal value: CA 2006, sec580. Except for this rule, the amount a company charges for the shares it allots will primarily be a matter for negotiation between the company and those buying the shares.
(1) Three people set up a new company and agree to put £5,000 each in as share capital. The shares will probably be issued at their par value, i.e. each will get 5,000 £1 shares, giving the company a total share capital of £15,000 divided into 15,000 shares of £1 each.
(2) Five years later if the company has been trading successfully and they have agreed to admit a fourth shareholder, the amount the newcomer will be expected to pay for the shares to be issued to him will depend on the current value of the existing company. This is always difficult to ascertain and will depend on the company's asset position, its profitability and the expectations for its future growth. If, say, an agreed valuation for the existing company was £60,000, the existing 15,000 issued shares would have a market value in the region of £4 per share, and they would negotiate around that figure as a price for the allotment of new shares for the new investor. If the shares are allotted at £4 per share, they will still be £1 shares, but issued at a premium of £3.
If a company issues shares at a premium it must set up a share premium account: CA 2006, sec610. This is frequently misunderstood. It does not mean that the amount of the premium has to be put in a separate bank account. It is simply a balance sheet entry that is subject to statutory rules which require this amount to be treated in much the same way as share capital.
Note that the amount charged for the shares need not all be collected when the shares are issued. In a private company, there are no requirements as to the amount shares must be paid up. A PLC must receive at least one-quarter of the nominal amount of the share and the whole of any premium when the shares are issued: CA 2006, sec586.
Note also that shares may be allotted for consideration other than cash.