Fruit trees in waterlooged soil

Willow is the only thing I can think of that likes it wet, and that doesn't fruit.

Can you make small raised beds or use open bottomed pots on top of the wettest area and plant your trees into those. Make sure that you don't try to change the natural run-off though.

Blueberries and cranberries like heavy, acid soil.
Quince rootstocks (onto which pears are grafted) also tolerate heavy soil.

But you'll probably find that almost no plant will survive if it is submerged for several consecutive days because the roots literally drown from lack of oxygen. Roots remain active almost all year round. Often the greatest root growth occurs when the tree is without its leaves in the damp, warm soil of autumn, while it's transporting nutrients down from the shoots to the roots.

Alternatively just make a large mound on which to plant a fruit tree.

Chances are your apples were on MM106 which is notoriously prone to root diseases - these being exaggerated in saturated soil.

Apple rootstock MM111, M26 or M9 have the best chance of surviving in heavy soil. But death in heavy soil can be due to fungal root rots or to lack of oxygen.
The M26 and M9 cope less well than MM111 when it's lack of oxygen, while MM111 copes less well with fungal attacks compared to M26 and M9. However, MM111 has a curious root structure and a very rapid healing ability which gives it the best chance of recovery, overall, from root problems.

Very few trees (mangroves apart) will survive if their roots are permamnently submerged in water. They will simply drown.

In some situations, taking out a planting hole is simply taking out a sump. Provision needs to be made fro the soil to drain.

My own observations - supported by observations of other fruit tree growers - are that the apple varieties which go dormant earliest, or which flower latest, tend to be a bit less troubled by root diseases.
This being because an early-into-dormancy tree may not be as active (hence less oxygen demand) during autumn flooding, while a tree late into leaf may not be as active during spring flooding; allowing the ground to drain and dry for a little longer.

Rootstocks M9, M26 and MM111 are slightly early into dormancy (my MM111's are a good indicator of how bad a winter will be: they have begun shutting down for winter in early August in recent years!) and the M9/M26/MM111 are also slightly later into leaf compared to other rootstocks.

MM106 and M25 are very late into dormancy, and MM106 is also very early into leaf.

There also seems to be some evidence of certain scions performing better in heavy soil, and somehow offering additional fungal resistance to the rootstock - perhaps a phenolic antifungal substance produced by the scion and flowing through the sap. The cultivar "Grenadier" is thought to be particularly good (or should I say "one of the least bad") for heavy soils.

I also wonder whether below-average-vigour scions might be useful too, as they would put less demands on the rootstock than a vigorous variety like Bramley which encourages the roots to work flat-out to supply its tendency for rapid growth. Roots can't work flat-out if they are suffocating.

Fruit trees don't like standing water. Some rootstocks are better than others (the American G.30 rootstock particularly so, but not available in the UK). Some varieties are better than others. But ultimately it is never going to work. In this case prevention is definitely better than cure, so if you want to grow fruit trees here I think (as others have suggested) you have to somehow improve the drainage and lift them above the water table.

I wouldn't give up on apple trees. As others have suggested here, grow them (staked) on a mound - I'd go 4-5ft diam and 1 ft high if necessary, and make sure the area is grassed. Grass swards help in dealing with heavy, prone to water-logging soils. Not only do they help dry the soil out earlier in the spring via evapotranspiration, but greatly improve soil structure/porosity, and consequently drainage, in the uppermost soil horizons. Furthermore, according to MAFF ('Apples', Bulletin 207, 1972, p.77) 'some (apple tree) roots grow up into the surface soil under the grass and into the turf itself, developing a fine fibrous system in the upper layers of the soil which is normally richest in nutrients.' It's likely therefore that a fraction of the tree's root system may escape the worst effects of waterlogging and remain functional. With such a wet soil, you probably don't have to worry much about the downside of the grass competing for water in the summer, and, provided the sward is kept reasonably short, competition for nutrients shouldn't be much of a problem either.

It is my suspicion that the combination of unusually large numbers of fine roots, combined with fairly high vigour, allows MM111 to recover more easily than other rootstocks.

The huge numbers of roots make it difficult for pests, diseases, damage or drowing to kill them all. The fairly high vigour of this rootstock, combined with its prolific root production, then allows it to quickly regrow new roots from those which survived and the tree to recover quickly.
However, MM111 is at its best in slightly alkaline soil around pH 7-7.5 and is especially good in shallow, infertile and droughty soils where MM106 does not thrive.
In notably acid soils (acid and heavy often go together) MM111 may increase the risk of bitter pit.

Below are two pictures of young "maiden" MM111 apple trees, showing the large numbers of fine roots.

Had a proper look at the trees again today and noted the varieties - one is Grenadier, the other Arthur Turner. Both still appear to be alive, the small branches are flexible and green when snapped, and the Turner is producing small green leaves. Both trees came from Morrisons last season, and are probably two years old at most? By contrast the other three are expensive three year old trees bought from a grower, so may be of a higher quality. Thank you for all the advice, I'll see what I can do for them. Been considering digging down a couple of feet next to them and installing a puddle pump, to siphon off the excess into the storm drains.

If the trees have only been in a year or two and are only small, it might be easier to dig them up in the next couple of weeks, amend the soil (building a mound is the best way), then replant them.
It's probably better to do upset them now but from which they'll recover from the transplant shock, than to leave them to suffer and the near certain death within a few years.

Dormant season is the time to move them. Some fruit trees will already be coming to life. Apples are a bit later than plums or pears - but you only have a few weeks to get it done.

FB - have you ever written a book? I'd buy it.

Me too also!!

I've got a couple of plums to plant tomorrow, spent a while down in the orchard trying to work out how to make a mound out of splosh. I think our soil is self-levelling at the moment