Depends on the width of the bed and the amount of sun it gets.
I'm not very good with compass points and where the sun is in relation to east and west etc..
I get sun all day, apart from shade which is man made by my neighbours 8ft high fence and wall, so have not needed to get my head around South East facing walls, If you say what time you get sun in summer and for how long I'd be better able to advise
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The wall should not be an issue providing you get alot of sun and double dig in manure at the start and then give the soil a dressing each year to provide a feed for the plants you plan to plant. I put in a 6ft high trellis a ft in front of the nieghbours wall/fence after removing two conifers which were as tall as the house, it's a flower bed now with climbers.
I don't see any reason why you can't grow cordons and plant veg in front.