Depends what you mean by a secret will. If you mean that only you know about it - I suppose the answer is yes, if you're careful.
I recently made a will and all I got was a letter from the solicitor, with the draft copy of the will, which I then had to go down and sign. A few days after signing, I received a copy of the will itself, so I can't see why you couldn't do it. You'd just have to make sure that if anything happened to you, you'd left something that would let people know that you'd made a will (or recently changed one) and where the will itself was being kept.