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The going rate for preparing a Deed of Easement is £850 to £1,000 plus VAT, I'm afraid to say.
It is therefore going to be a lot quicker for you to proceed with the Deed being drawn up. You may be able to argue that you have a right of necessity but this is going to take an awfully long time and unless you have the relevant expertise, it would cost more than £1,000 in Solicitors fees to pursue this, and there is no guarantee you would be successful.
I am not sure why the Deed was not executed upon you buying the property,but unless you authorised your previous Solicitor to proceed without it being in place, then he may well have been negligent. Unfortunately, you only have 6 years to pursue a case of negligence, and so if you were aware of that no Deed had been drawn up in 2000, then you have lost your right ot sue your previous Solicitor.
I am sorry this is not the answer you wer elooking for, but hope I have answered your question.