I used to breed chickens a few years ago, so I think I have some sort of expertise.
Mostly it depends on the size of the garden, but also the housing. Yes, Eglus and similar are okay, but only in the "meets the minimum standard" sense. IMO, the perches ore often far too low- for the best air flow and for the birds to feel comfortable there should be about 18" of a gap under the perches. That's without issues regarding temperature as a pp has discussed.
I'm assuming you will have a covered run- will you be able to move that? Chickens will strip any grass or other plants down to bare earth in no time flat. You can't just let them live on mud, so ideally you should move them around frequently. Mine were free range over 10 acres, so it was never a problem, but it will be in an average garden. Not moving them will also encourage a build-up of parasites etc.
If you do go ahead, you will need to be careful about rats. Houses on legs can help with this because the heat doesn't attract them so much and it's harder for the rats to get it. Also, ad lib feeding is a bad idea, you should only feed as much as the chickens will clear up in 10 minutes at each feed.
I think what you are planning is possible, but certainly not the best life for the birds.