I assume you're showing two sides of the same ring. Unfortunately, there's not a lot to go on here. Your friend is essentially correct. The 'broad arrow' or 'pheon' mark denotes that whatever this is, or belonged to, it was government property. The mark is most usually related to the "Board of Ordnance" who issued contracts for the supply of arms, ammunition and other equipment as well as provisions for the British military... both navy and army. The trouble is, it has been used for a very long time (since the 14th Century) and for a huge variety of items.
I would suggest contacting the British Museum in London to see if they can determine what it might be. I have always found them to be very helpful. The relevant department and its email contact address are at the link below:
There's more information on how to request identifications at this link, and note that the total size of emails (including attached images) should not exceed 2MB:
Note that the Museum of London, while a great source of information only provides a contact form, not an email address, for online enquiries and you can't attach pictures... so it's less easy to get their help. They will also be closing for a while from 4th December, in preparation for the museum moving location so I expect the curators will be rather busy.
