The data is based on casualties, but I think there are some points masking the issue:

1. Traffic is slower due to the decreased speed of traffic because of increased number of vehicles, and they continue to improve their safety (i.e. with proximity sensors & cameras). It's likely we see a reduction in casualties and fatalities even if number of accidents in total increases. For example, the number of accidents on the M25 may go up, but whilst they have speed restrictions for large areas of 50mph and sometimes 40mph, casualties will be decreased.

2. Payouts for minor injuries such as whiplash were pretty much stopped by insurance providers. Historic figures are likely inflated and new figures are likely deflated due to claims not being accepted.

3. Due to the cost of living and insurance hikes, we likely see people try to avoid making a claim. If a claim is made, the insurance premiums for both parties is increased (no matter who is at fault), both parties can be without a payout for a long time, the vehicles may be categorised and lose their value. If both vehicles are still drivable and an agreement can be made, the entire incident can go without being recorded.

The problem with proving the above is the linked data you have is for casualties, and insurance claims data I believe will reflect similar issues. I'm not sure how you would encapsulate people who have an accident but refuse to make a claim. Perhaps motorcyclists and pedestrian casualties may offer a ground-truth, as either rarely have a collision involving a vehicle where there is a choice to not make a claim.