From the UK, I do know how you apply for a will. First thing to check is, have you checked on Ancestry's National Probate Calendar that your person left a will for probate? If you're positive you've found the right person, you need to visit the Probate Registry in London or write to them at
"Principal Registry of the Family Division
7th Floor
42-49 High Holborn
First Avenue House
Holborn
London
WC1V 6NP", including the details of who you want, date of death, place of death and date of probate grant. Therefore, they will require a form of payment of which they will include details of in a reply letter. I live quite far up North from London, and wrote to them to order some wills. I was very pleased with the instant replies, and their ways of satisfying customers. Overall, good service and kind staff.