Partial Sunny Garden help

Hello There
I have just discovered this wonderful website and promptly joined up.. I am fairly new to gardening but have planted lots of vegetable seeds this year already.
The problem i now have is that they need planting out ( i hope this is the correct terminology) My garden is East facing and without digging up all of the left hand side of my garden for the plants, i have no idea what or where to put them.
All of the sunny side ( the left) already has bushes ( established) and my lettuce and cabbages in it.
I have Tomatoes, Sweetcorn, Sprouts, Leeks, Peas all still needing a home...Has anyone any ideas please of where to place my beloved plants? I wondered about somehow hanging them on the 6 ft fence i have at the left ( sunny side) but really have no clue. I realise i can use growbags for the Tomatoes but, again without using space on my lawn, i have nowhere..
I look forward to your ideas, and Thank You.

 

Welcome to Gardeners Corner Yorkiepudding,
this space problem is one that all us keen gardeners are faced with. There is no magic - you have to sacrifice one for the other - or win the lottery and buy a DES.RES. with a few acres. There are tomatoes for containers which could go on the fence, and they will really enjoy the sun. Not the other vegetables though I'm afraid,