Well, that's a bit confusing - you're in the UK, which must mean your apple and plum trees have no leaves at all currently, so there's no point in spraying with anything now anyway. If you've got these sort of fungal problems, hopefully you cleared away all fallen leaves from around the trees last year - if you didn't, do so now. Suggest you wait and see what problems crop up this year - you haven't said whether you saw powdery mildew or another form of mildew on the leaves, and as for 'black spot', that's not a common affliction on fruit trees, so that's likely to have been some kind of leaf spot, either bacterial or fungal. It's important to establish precisely which problem you're looking at before attempting to treat the trees.

The link below is to the RHS latest on the availability of fungicides and what they're used for

https://www.rhs.org.uk/advice/pdfs/fungicides-for-home-gardeners

OK - now is the perfect time to address these issues because NOW you can actually do something about them. Don't just wait passively to see what happens. You already know what's going to happen - black spot and powdery mildew! If nothing changes, nothing changes! You want to enjoy delicious apples and plums this year - not play 'hit or miss.'

Black Spot & Powdery Mildew are indicative of poor air circulation & insufficient sunshine. If the trees aren't too big, consider relocating them to open space where they get full sun and the open breeze. This will eliminate these problems by a long way - You should do it NOW, before they leaf out and break dormancy. Doing it now would reduce transplant shock if this is feasible for you to do. Maybe hire some help.

Thin out the canopy to get more light into the crown. Now is the best time to prune because you can make precise cuts to remove unproductive branches and open it up to more light and air. Prune out all suckers, any branches that crisscross and rub against each other, dead wood, and any branches growing directly into the center of the canopy. You can see what you are cutting.

If you can't transplant, cut away all surrounding trees, bushes, etc. You want to increase the amount of open space and light as much as possible. Clean up all debris, leaves, grass, etc surrounding the trees.

As an alternative to the fungicides, you can make a mixture of baking soda (baking soda, bread soda, cooking soda, and bicarbonate of soda) and water and completely spray the trees. Do it early in the day - morning if possible. I hope you find some of this useful. Good luck!

ps. Take a look at my apple blog. Notice how each tree is open to the sun and has full air circulation 360 degrees around it - no competing vegetation at all. No mildew problems on these trees at all and they all have a huge bounty of delicious fruit. Try to duplicate a similar situation for your trees, plums too.

link to my blog: http://www.growsonyou.com/bathgate/blog/29118-apple-blog

Kirkbylot, I take it that a certain kind of fungicide was recommended to you, and many of the old standbys have become illegal over the past decades. There are many other fungicides still available. I would only use a chemical fungicide as a last resort, however, between damage to the environment, and the chance of breeding resistant strains.
Although Bamboo's point is well taken, a light fish oil or vegetable oil spray would kill the spores overwintering on your tree, though that doesn't keep them from blowing in from your neighbors' trees later in spring. Bathgate's suggestions are all good, too. Applying good compost to the soil to bump up the earthworm population will also help the trees to resist disease.

I agree with all the aboves, but, I would not prune a plum in winter, wait until late spring/summertime - or you may add silver leaf to your diseases!
Airflow is really important, better to radically prune and keep the trees in a restricted shape if you cannot improve the site any other way. But after pruning it will encourage the tree to make lots of 'water' shoots - so you need to be really diligent with summer pruning on the apples and later summer for the plums.
As most of my fruit trees are arched cordons, and the few that aren't, need to be kept fairly low for cropping, I prune twice a year, winter and summer for apples, pears and quince, late spring and late summer for stone fruit - as needed. Even so my cherry tree (supposedly on the most dwarfing rootstock available) is busting out of the fruit cage!