for a 1/4 mile car you want low low weight and big Hp but weight first and formost.
Kit car is the best way to go with a bike engine.
I have a similar project planned for some future hypothetical time when my finances are better.
Back in the 80s Suzuki sold a tiny little front-wheel drive utility in this country as the Mighty Boy. They only weight just over half a tonne, and a couple of people have done electric conversions of them by chucking the engine/transmission unit and fitting an electric motor, then removing the floor of the tray and fitting a re-inforcing frame in there that holds the batteries.
My idea is to do something similar, but fit a 1.3 litre Suzuki Hayabusa bike engine/transmission in the back instead, with rear drive.
So it'd look basically standard, especially with a tonneau cover fitted. But it'd be light at barely over half a tonne. It'd be rear wheel drive with the engine/gearbox over the drive axle for traction. Even a standard Hayabusa engine produces pretty close to 200 bhp, so you'd be talking quarter miles in just over 12 seconds. With a bit of tuning work it'd be down into the 11s. With a turbo, which are available, it'd be down into the 10s.
And with it being so light I'd be able to fit an A-frame towing rig to it and tow it down to the drag strip behind the Clio Sport, so I wouldn't need another car big enough to tow a trailer to carry it.
I don't see any Mighty Boys on UK eBay. But its a derivative of Suzuki kei cars of that era so I presume an early Alto (?) 3-door hatchback would be about the same weight and have the same ability to have a bike engine fitted in the back with some cutting and strengthening.