Travelling to Pembrey in South Wales, Hills had set the target of returning home with maximum championship points.
In the first heat, he came away with the fastest heat time of the day and the second heat concluded with a similar result.
In the third heat, he was beaten into second place by reigning champion Tristan Ovenden but his performances put him on pole position for the A-final.
After a red flag incident at the first corner, the final was restarted and, in the rush to the first corner, Hills was spun around after contact, which left him in last place.
He managed to claw his way back up the field to finish sixth but Hills said afterwards: “I’m just really disappointed with the outcome after such a promising start to the day, especially as it was the first time I’d been at Pembrey.
“Putting the car on pole for the A final, I definitely had the pace to win the meeting, but then that’s racing, a bit of contact at the wrong time turned me around and ended my weekend.
“I’ll be fighting harder than ever for a win at the next race. We still have a lot of time to find in the new car, considering that it was only the second time I’ve been in it.”
The championship now heads to Mondello Park in Ireland for a double header on June 27 and 28.
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