There is no specific format for a disclaimer.
Whilst it might be preferable for the individual to complete a deed of disclaimer, a letter clearly indicating the intention to disclaim is sufficient provided that it does not allude to any other formality or seeks to direct the legacy elsewhere.
The issue with a letter is that, generally, the beneficiary has not sought legal advice as to the effect of their disclaimer and there is a risk that, at a later date, they could seek to revoke the disclaimer, arguing that it was a “mistake”.
If, as stated, the beneficiary wrote to say they did not want the legacy, and has ignored all subsequent communications I would be inclined to the view that this supports the intention to disclaim and proceed on that basis, having made a clear note of the reasoning and keeping together all the communications in case there might be a subsequent change of heart by the disclaiming beneficiary.
The only caveat I would add is whether you are satisfied the individual received the follow up communications. Have you been able to verify that they continue to live at the address to which you have been writing? If they have lost capacity, or died, I would have expected that whoever was looking after their affairs/estate would have picked up on the communications and, if they wanted the legacy to be paid over, made contact.