Thanks for all the replies.
By a 'take it or leave it approach', I mean not cooking family meals based largely around what your child will eat (or not offering an alternative if you're making something they may not want).
I guess my intention hasn't been to prevent fussiness, but to (a) get him used to trying a wide range of foods and (b) not have food as a control issue.
I think the blood sugar thing is a big part of our problem. I do give him snacks every couple of hours - but if he refuses either the protein or the carbohydrate at one meal (or refuses the snacks available), he will be in meltdown by the time we get to the next snack/meal time and will then be amenable to eating even fewer foods (other than fruit).
I try to give him a choice over snacks and lunch.
I try to avoid letting him fill up on fruit as it doesn't keep him going for long enough. Protein is what really helps (as it does for me) but he doesn't always want it.
When I offer alternatives, it's either as a normal part of dinner (I cook fish for us, fish fingers for him but get him to try some of ours - or cook potatoes for us, pasta for him) or I offer a nutritionally equivalent alternative afterwards. So yesterday he wouldn't eat any of the chicken which was for dinner. I said, "Okay, as long as you've tried a piece, you don't have to eat it." He then ate the rest of his dinner (pasta). At the end of dinner, I offered him some cashew nut butter which he ate.
He is allergic to, or his eczema is irritated by: most nuts, coconut, egg, banana, cucumber, melon, kiwi, tomatoes, citrus, chilli, spices, baked beans, sesame. He doesn't like: fish (apart from shop-bought fish fingers or tuna), potatoes, any veg (apart from - sometimes - raw pepper and celery), cous cous, legumes, cheese (he'll only reliably eat it as cheese on toast or in homemade cheesy biscuits) or milk (other than on cereal). I'm intolerant to wheat and dairy, which makes family meals even more complicated. 
DS does bf, although I don't think he gets loads of milk as he only has 1-3 feeds a day, and I'm 8 months pg.
A normal day would be:
Breakfast - porridge with fruit.
Snack(s) - cheesy biscuits, cashew nut butter sandwiches (which he'll only sometimes eat), oat biscuits, cream crackers, fruit.
Lunch - cheese on toast (though he seems to be going off that now), fruit.
Snack - as earlier.
Dinner - pasta or rice with meat, fish fingers and a token tiny piece of whatever veg we're having.
Snack (if dinner wasn't immediately before bed): as earlier.
From what people have said, I'm guessing that more of a take-it-or-leave it approach may not be any more successful than what we're doing already.