Not true, even by your source. In 1995 (the last year of the double-nickel) the number of deaths was 41,817. Four years later, road deaths had indeed climbed all the way to 41,717, an "increase" of -100 deaths. Basically, it bounced around from about 41,000 to 43000 up until 2007, although because the population and miles traveled were increasing, the per 100,000 population and the per mile figures continued to decline. Then it took sharp and sudden dips in both 2008 and 2009, down to about 33,000. It has only recently (2021) bounced up to the 43,000 level again, which, yes, is the level of 1985, just in raw totals, but is far fewer per mile or per capita.
ETA: The UK is certainly to be commended for its low motor vehicle fatality rate, but I do note that you have achieved this despite not having significantly lower speed limits--70 MPH on motorways.