Kilmarnock Willow Keeled Over

I have a Kilmarnock willow that has, from some combination of wind,
rain, soggy ground or whatever, keeled over and is now resting
somewhat crazily on its "canopy". It's about 18 years old and looks
(otherwise) very healthy.

A brief examination reveals that it's still fairly firmly attached to
the ground as if there is some central tap root. However the roots on
the side from which it has tipped have lifted from the ground and seem
somewhat shallow. There is no evidence of roots ripping off -
everything looks very wholesome, just lacking in mud/quantity/depth if
you get my drift.

Nothing in any of my books answers my (I hope) simple question - does
a Kilmarnock send out a tap root? If it does then it might be worth
trying to "re-erect" it by attaching it to a stout stake for a few
years to re-root.

If there's no tap root as such then I'd guess that the tree is simply
attached to the ground because it has rooted more strongly on one side
for some reason and I suppose it would be better to dig it up and
replace it.

Any advice would be appreciated. Thanks in anticipation.

Cheers, Jake
Urgling from the East End of Swansea Bay where sometimes
it's raining and sometimes it's not.