There are different types of domains
.nhs.uk domains are free of charge but subject to NHS naming conventions (no abbreviations and usually need to include a location ie MySurgeryLondon.nhs.uk). They may take a short period of time to be released.
.co.uk domains are free for the first year then £20+vat per year added on to your annual invoice. These domains can contain any text, numbers or combination of both. They can be purchased and configured immediately as long as they are available (this also applies to .uk, .org.uk etc - anythig that ends in .uk that is not an nhs domain).
.com .org .net .info etc these domains are often have commercial or international connotations so are less popular. The cost and qualifying criteria are the same .co.uk
specialist domains Other domain types are available but are often extremely costly and have a number of rules associated with them. Please contact the the support desk for help with these.