Here is an update: I've not yet found a living relative of Horace. Four things are making it difficult to find information on people living in the U.K. are: 1) the strict data protection laws; 2) so far it appears Horace only had one child, and she neither married nor had children; 3) Many of Horace's siblings died before reaching adulthood - so they did not have children; 4) the family trees on Ancestry and FamilySearch that include Horace are mostly incomplete. Despite these difficulties I will keep researching and calling people. If I, and all other efforts, fail to locate Horace's next of kin you may want to consider donating the fork to the Coldstream Guards Association. If interested I can introduce you to my contact.
British Telephone directory: found people with the surname of Astin in Burnley and Poulton Le Fylde. If my other research doesn't result in the next of kin then I will begin calling these people.
St. Peters Church: Fr. Andrew Holmes, the Rector of St Peter's Church in Burnley, where Horace was married and daughter baptized, replied saying they continue to look at their records for Horace's next of kin. He added he'd get back with this coming week. If I don't hear from him I will send a follow-up email. Also, I shared with him the names of the people in Burnley with the surname of Astin and asked if he heard of/knew any of them. Unfortunately, he did not.
PHH Solicitors: I’ve spoke on the phone 2 more times with the staff of PHH Solicitors but have yet been able to speak directly to Helen Springthorpe (the Administrator of Enid's estate). Her secretary did confirm that Helen got my emails and will talk to her again about replying.
Preston Family History Centre: This is the closest centre to Burnley. At their request I emailed some questions. Their reply did not include the identity of a living relative of Horace. It did however include their findings and some search tips – which I pursued to no avail.
Blackpool England FamilySearch Centre: This centre is the closest to Poulton Le Fylde, where Enid passed away. Yet to get a reply to the questions I emailed them. Like Preston, I may resort to calling them.
Inner Wheel: My contact indicated that there is an Enid Astin that belongs to the Elland Chapter and she will try to get in touch with her. Although that Enid is not Horace's daughter, she may be a relative.
Find-a-grave: Been examining records of people with the surname of Astin buried in Burnley cemeteries. Thus far, none list children and obituaries.