I understand it is possible to deduct the costs associated with the raising of new equity from the equity. Can you confirm this, and if correct how is it dealt with from the point of view of each shareholder?

If you look at HMRC’s Business Income manual (here), you can see that the expense incurred in the financing of a business through share capital is likely to be capital expenditure. Similarly, the expense incurred in the raising of money in the form of debentures is capital expenditure. This is a company expense and does not directly impact on the shareholders at all.