You need to make your " border" ( not a hedge ) much wider and move it in bit.
So leave a strip of grass wide enough to get a lawn mover down, maybe about 1 meter. That's the " path " for pedestrians to step on if necessary.
Then clear a space for your border, it needs to be at least 1.5 meters wide. If you have plenty space I'd make 2 or 2.5 meters. Then plant with a range of plants as suggested above. Mostly shrubs with some perennials in between. You want fast growing easy shrubs with a variety of shapes and leaf colours and at least one third evergreen.
If you can tell me the conditions in your garden I can suggest some other shrubs for you. So is it sunny or shady , windy or sheltered. Where are you in the country ? If the soil sandy or clay ?
Once you have finished, put chipped bark down on every single bit of bare earth between the plants.
You will neee to water after you plants and then throughout this summer any time it's dry.
This will cost you time and effort . Stripping the grass from the area to be planted is very hard work . Stack the turf upside down in a corner someone behind a shed as it will make lovely soil once it's rotted down.
Plants will cost money.
But it will look lovely in a year or two and will keep people off your garden now.