Thanks for your question.
If there was no tenancy agreement and you did not pay rent then I'm afraid that you have very few rights at all and were in fact staying their only on licence.
One right that you do have is the right to receive "reasonable notice" of eviction. 28 days is usually sufficient for these purposes so were they to evict you after the notice expires the eviction itself would not be an illegal one. There is no option for you to apply to court for an extension of the notice so you're going to have to deal with the executors directly.
I would write formally to them impressing upon them that you do not see your occupation of the property as any kind of long term solution and appreciate that you must move out very soon, but you consider the notice length to be unreasonably (though in my opinion it is reasonable) and asking that it be extended by, say, two weeks due to the time of year and your workload making it not practicable. .
You should at the same time assure them that you will permit any viewings of the property, shall keep them updated as to your progress with finding a new property and shall vacate earlier than your suggested extension if you are lucky and manage to find a property to move in to. I would expect them to be understanding.
If you know the residuary beneficiary of the estate then you may choose to appeal to them, though the executor's have complete responsibility over the estate and this issue they may listen to any representations made by the beneficiary in this regard.
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