What is the test for a right of action under the statute of 1540 for damages arising from a covenant which does not run with the land?

In Re King, supra, Lord Denning discusses the distinction, in this context, between covenants which run, and do not run, with the land (at p. 481). In the class of matters which do not run, but remain with the assignor as “ 'merely a chose in action' sever from the reversion”, Lord Denning places a right of action on a covenant to pay compensation for damage done to the land by a lessee having the right to mine for clay: Martyn v. Williams (1857), 1 H. & N. 817, 156 E.R. 1430. But Lord Denning observes that the right to sue on a covenant to "repair" or "re-instate", in respect of depreciation which had occurred during the assignor's time, that is to say prior to change of ownership, fell into the other class. He explains the distinction (at p. 480) thus: If the covenant to repair or reinstate had been performed, the advantage of it would have accrued to the heir or devisee and not to the executor. It was only right, therefore, that when the covenant was not performed, the heir or devisee should have the damages for nonperformance. It would obviously be wrong that the damages should go into the pockets of those entitled to the personal estate. The loss had not accrued to them, but had been suffered by the heir or devisee of the real estate. I understood counsel to be agreed that Lord Denning in this case correctly states the law under the statute of 1540.