When I got my visitor's visa handed to me, I was 15. I am now 16, and I must travel to England alone. However, my visa states that it is only valid if I am accompanied by my mother. This cannot be arranged. I can get her written consent, and the written declaration from my sister (she's 25 and lives in the UK) whom I will be staying with that I will, in fact, be staying with her. Would this work, or would I be denied entry? I had already purchased a ticket, not aware of my visa's status. My departure's on the 15th of June.
The visa condition "...only valid if accompanied by mother..." is clear and unambiguous.
The first hurdle will be the airline's assessment for boarding when you check in at the departure airport. The visa condition is straightforward, and will not be satisfied by the mother's written statement — a piece of paper is not the same as your mother in person. Because the airline's check-in clerk will see that you do not meet your visa's conditions, the airline will not allow you to board your flight to the UK.
There's nothing magic about the age of 16. That you have a visa suggests that your passport requires a visa for entry into the UK. Being over 16 won't change this.
Thus, I expect the airline will deny boarding, and you won't even get to the UK border. It would be wise to explore alternative travel arrangements.