Wikipedia's entry for 1898 mentions Mr Henry Lindfield as being the world's first fatality from an automobile accident on the public highway. Here are some newspaper reports of the incident.
Mr Henry Lindfield of Linton House, Brighton, was riding from London to Brighton, on Saturday, on a four-wheel motor waggonette driven by petroleum with electrical ignition when the car swerved in Russel Hill Road, Purley. It then ran through a wire fence against an iron post, and pinned the unfortunate gentleman against a tree. Mr Lindfield was released and taken to Croydon where he died from his injuries on Sunday morning.
— The Newcastle Courant, 1898-02-19 page 3 column 7
A Motor Car Fatality
On Saturday afternoon Mr. Henry Lindfield, Lynton House, Montpelier Street, Brighton, was travelling in company with his son in a motor carriage at Croydon. In Russell Hill Road something went wrong with the apparatus, and the vehicle ran on the path. Mr. Lindfield's leg became jammed against a fir tree, and he sustained serious injuries. At Croydon Hospital the limb was amputed, but the injured man succumbed to shock to the system.
— The Illustrated Police News, 1898-02-19 page 5 column 2
Mr. Henry Lindfield, of Linton House, Brighton, was riding from London to Brighton on a motor car, when it ran through a wire fence against an iron post and pinned him against a tree. He died from his injuries on Sunday.
— Lloyd's Weekly Newspaper, 1898-02-20 page 15 column 1
A much fuller account, referenced by wikipedia, is over here. But this account mentions Bridget Driscoll who, two years earlier, had been run over and killed by a car. She may not have died on a public highway but - and not to take anything away from Mr Lindfield - it seems to us that he - a motor vehicle geeque (it's the nineteenth century dammit) - was less of a victim than she.
But you might also want to consider Mary Ward in 1869.