The prime qualification for admission into the Royal Arch is to be a Master Mason, of at least four weeks standing, in a Lodge under the United Grand Lodge of England, or a Lodge under a Grand Lodge recognised by it.
As in all other Masonic Orders, you will need a proposer and seconder who are members of the Chapter in which you seek to be exalted. If your Lodge does not have a Royal Arch Chapter attached to it, it will probably have an arrangement with a local Chapter. Check your Lodge summons which may give details of either the Chapter attached to it, a Chapter to which it supplies candidates or a member of the Lodge who is a Royal Arch Mason who will assist members interested in joining the Royal Arch.
If there are no details on your Lodge summons, you can usually identify the members of your Lodge who are Royal Arch Masons as they will normally wear the jewel of the Order with their Craft regalia. They will be delighted to be approached about membership.
If all that fails, in London you can contact the Metropolitan Grand Lodge office, and in a Province or District the Provincial or District Office respectively.