Although the statute of limitations is 6 years for debt collecting and a person can go to the small claims court to collect money for 6 years if the amount is extremely low i.e a few hundred pounds your landlady will probably not enforce anything.
I would furthermore ask her what evidence she has to suggest you shortchanged her asking for it to be presented clearly. I struggle to see how someone can JUST pick up on an outstanding debt after 3 years. Most businesses must fill out tax forms and do yearly accounts. Everything seems a bit fishy to me.
I would furthermore notify her you will be contacting HMRC on both of your behalves as this change in money owed could effect the amount of tax you paid. Although normally a tax return cannot usually be revisited However, under what are called discovery provisions, it is possible for the tax office to re-open tax returns that are twenty years old if they suspect fraud or neglect. For example on incomplete disclosures which this would/ could be.
In most instances, the statute of limitations for an audit concerning under reported income is three years from the year the income should have been reported on the tax return of the person who earned it. So she could have done this to avoid certain taxes and by not declaring the change depending on the amount, did you sell the business e.t.c it could seem like you aided in fraud.
Maybe I am over thinking this but good luck and try looking into getting advice from citizens advice, HMRC.