Garage has to be set back by a meter

It probably wouldn't hurt to show your plans to all your neighbours, as it's a small street you could show it to everyone in the street, if they all like it you can get them to sign something to show the council that all your neighbours think your plan is "sympathetic" to the streetscape, THEIR OWN streetscape. That might carry some weight. Might not, but it couldn't harm your argument at all.
You could also try adding a front porch that comes out 1m in front of the garage, so the front of the porch is technically the front of the house, however that would depend on whether you are already at the minimum setback with the garage. At the very least, doing this might mean you could have the garage level with the rest of the house instead of 1m back. So you are getting at least 1m of backyard back.

I think it's worth trying everyone's suggestions. It's not only about the logic of your argument, and I reckon you've got a good argument, but about showing that your determined and well-prepared and won't be fobbed off.

Move the meter forward two metres, and all is then good?

*bad internet spelling pun boom-tish*

Yes, after moving the garage the whole thing works out perfect. Move it back one meter and I would waste a lot more space on the backyard then those meters. This is why I want to work around this silly rule.