Where to plant apple trees????

I'd love to grow 2 semi dwarf apple trees (3m max height) on my plot - the question is where?? They need to go in soonish. Obviously the rasps & asparagus and strawbs (2nd year) are fixed, brassicas can't be disturbed yet (PSB). Each row is 10 foot wide, very slight slope, hence the waterlogging in bed 1. There are no rules against trees and have mentioned it to my neighbour who didn't raise any objections - any ideas peeps?
(measurements are approximate - plot is about 10x 45, clayish but improving slowly)

Bottom end next to bed 1 is a Bramble patch about 12 foot (!) behind which new plots are being marked out at this end, turf paths up both sides (rectangular plot) and road at the other end next to flowers)

Fallow currently digging over for spuds, poor drainage in winter, ditch at this end About 10’ wide by 8’   BED 1

BED 2  10 X 3Winter lettuce IN         mange toute last year Runner beans last year

BED 3  10 X 4 Parsnips/beets & carrots last year Sweetcorn/courgettes                        Pear tree – useless, no idea what type

LINKABORD1m sq raised bed Will have herbs this year      BED 4   6X4' Asparagus x 6, 3 more to come

Autumn bliss raspberries x 12 BED 5  10 X 4

Brassicas & leeks    BED 6 10 X 6'

Broad beans  BED 7 10 X 10
Garlic & Japanese onions
(Will plant mangetoute, courgettes & sweetcorn lLater)

Rhubarb   Strawberries x 3 varieties
Dahlias/daffs/lavender along front edge

Thanks mum, The most obvious place would have been bed1 next to the bramble patch so as not to shade too much, but it's going to be way too boggy in the winter.
As the kids aren't too fussed about veggies, but love apples i was going with the "grow what you all like to eat" mantra, I might end up with a nice seat underneath them and a bit of grass, but less room for big crops like squash, courgettes & corn - hmmmmmmmm!!

The additional raised bed for the apples sounds a good solution 

Love the idea of a bench, but would you have time to sit on it Janey? 

You are right that the ground under the raised bed could puddle, but wouldn't the ground itself puddle anyway unless you dig a big hole and fill it with non clayey soil 

Thanks for your ideas, all. Tried to dig today, no way was anything getting through that soil today, even at 4 after 8 hours of sun on it - there's always next week, or the week after - meanwhile I've 15kgs of seed spuds chitting!!