Repairing my front step- suggestions ?

usignuolo

I live in a semi detached Victorian house with a tiled front path (Victorian encaustic) leading to a front step which gives access to the open porch and front door. All the other houses in the road have a York stone step at the end of the path where you step up into the porch.

I have, for reasons best known to the previous owner, a sort of concrete box painted white, completing enclosing the original step. So it just looks like a white box filling in the porch. (my neighbour thinks it was installed because the original stone step up to the porch broke).

Sadly, for me at least, the concrete slab step I inherited, which is painted white, is full of crevices, cracks and "dimples". So however often I repaint it, it isn't long before dust settles in these imperfections and it looks shabby again.

To date my efforts to entice a builder/specialist, to replace it with a new York stone step, have failed. They all take one look and announce they are busy. My search continues but meantime I should like to at least give it a smooth surface.

I could cement it over, or use a Polyfilla product which has a plastic content which forms a sort of skin over the rough bits. In the case of the former (cementing it over), I am concerned there would not be a key for it to adhere to. In the case of the Polyfilla plasticised coating, I fear it would crack and peel if there was a severe frost, or indeed if a large object was dragged across it. (Not impossible where the OH is concerned.)

Any suggestions?