There could be a number of reasons why probate has been delayed - from litigation to apathy. However, unfortunately, you have no "locus standi" (ie legal standing) to hurry things along as you are neither a creditor or a beneficiary of the estate. The only thing you could do (if it IS the case that there is some damage being done to your property as a result of the dilapidated state of the other property), is write to the executors and explain you are considering taking legal action against the estate.
However, in reality, unless there is something escaping from the property (say water or sewage) onto yours or it is falling down and pulling yours with it, I do not think that you have an actionable case against them.
The only other thing I can think of is to check the deeds of the property with the Land Registry (you can only do this if registered land). There may be a covenant which is being breached, but that is a very long shot, and I doubt there will be any such breach.