Gorgeous house OP. Love your style.
You're right in that the garden is the issue. Compared to the house, it's a huge let down, as is the bit at the front of the house. I know you've said you use it for parking, but with such a small back garden, I think you need to make the most of the space out the front too.
Outside the front door, you need some colourful planted up pots, hanging baskets etc, to create a little oasis of greenery. I'd also put a big rectangular planter under the bay window at the front, again, filled with lots of colourful plants, just to give the outside a bit of a lift. On street view your frontage looks barren compared with the lovely green lawn and beautiful magnolia of your next door neighbour. As the bricks of your house are still very raw and new looking, the whole impression is quite stark and cold - a bit half-built housing estate.
As others have said, the inside of your house is so immaculate, the garden feels like a total let down. It's all very half hearted and there's no sense of 'lifestyle'. For families the teeny tiny bit of grass with some slides squeezed onto it just emphasises how non-child friendly the garden is. It actually makes it look smaller than it really is, having that little splodge of grass. The mismatched garden tables, the randomly placed bench - it makes the garden look like a dumping ground for spare furniture rather than a lovely space to relax. I don't actually think the size is that much of an issue - plenty of people don't want a big garden as the maintenance is a PITA - and lots of people with older children won't mind a smaller garden as the kids will prefer to go to the park to kick a ball around anyway, so the garden can be largely a space for socialising and relaxing rather than playing.
In order to make the garden just as wow as the house, you need to invest in some decent garden furniture, fairy lights etc and set it up as a real tranquil oasis. A PP has posted some great photos of what it could look like. Get rid of the kiddie toys and get some grass down and plant up your pots with established, colourful plants/flowers. You might need to spend a couple of grand, but if you use pots, you can take everything with you when you move anyway, so you won't be losing any money.