The advice above will only work if the solicitor is the executor. If he is, you will, I think, only be able to complain if you are a residuary beneficiary. If that is the case go ahead but ask the Senior Partner (or better still the Complaints Handling Partner) to invoke his rule 15 in house complaints procedure. You must do this before you complain to the LS - else they will just write back and say "Have you done this?". If the solicitor is ACTING for a lay executor or you are a pecuniary legatee (ie you have been left a fixed sum of money, rather than a share of what is left) you have no right to complain through this route, since you are not the client, but I suggest an alternative below.
Unfortunately, in my experience, the Law Society Complaints division (I thought they were the CCS now - if they could deal with complaints as quickly as they changed their name it would work) put about as much fear into solicitors as a toothless tiger in this type of situation. However, when an executor swears an oath to obtain probate he swears to collect, get in and administer the estate which recites s25 Administration of Estates Act 1925. If he fails to do so (or fails to explain why) you can call him to account. My recommendation would be to write to the solicitor and point out that two years has now passed and they are failing to respond to correspondence. If you don't receive a response within 14 days you will have no alternative to apply to the District Probate Registrar for a summons under s25 Administration of Estates Act 1925 for an account holding the executor (ie not the estate) personally responsible for the costs. Although this won't necessarily result in the payment of your legacy, it will concentrate their minds significantly (the "personally responsible for costs" bit works every time) and you will know if there is enough money in the estate to pay your bequest. It won't cost you anything to issue the summons (I think) and you can act