Road casualty rates rose in the 12 months to the end of March because of more accidents involving cyclists and motorcyclists, according to government figures that have prompted cycling groups to demand action on safety.

The number of road users killed or seriously injured rose even more steeply in the three months from January to March, compared with the same period in 2013, although the comparison was distorted by the unusually cold start to 2013, which reduced the amount of traffic on the roads.

Overall casualty rates remain very low in historical terms – this was the second smallest number of deaths and serious injuries for a January-March quarter since equivalent records began in 1979 – but Department for Transport statisticians said they did not know why the rates were increasing.

Cycling groups said the particular toll among cyclists showed that ministers needed to invest in better bike infrastructure.

In the year to the end of March, road deaths totalled 1,750, up 4% on the year before, with the broader measure of deaths and serious injuries rising by 1%. Within the latter figure, the tolls of car users and pedestrians each fell by 1%, while that of cyclists and motorcyclists rose by 7%.

It is the latest in a series of road statistics in which cyclist casualties have risen against a wider trend of fewer deaths and injuries for most other road users. British Cycling's campaigns manager, Martin Key, said that cycling remained safe on the whole but that much more could be done.

"The fact is that our roads are not designed with cycling in mind, and these latest road casualty figures are a reflection of that," Key said. "Without adequate and sustained funding for cycling of at least £10 per head, coupled with real political leadership and national targets, Britain will continue to fall far short of great cycling countries like Holland, Germany and Denmark."

Road deaths in January to March this year totalled 380, up 13% on the same period in 2013, while deaths and serious injuries rose by 17%. Within the latter figure, the toll of car users rose by 15%, pedestrians 16%, cyclists 27% and motorcyclists 20%.

Some of this could be attributed to reduced road use – especially among cyclists and motorcyclists – during the cold start to 2013. The 2013 quarterly casualty figures were 15% lower than those for the first three months of 2012.

But the beginning of this year, though milder, was very damp, the DfT report noted. Overall, the reasons for the rise in casualties on both a quarterly and annual basis "aren't fully clear", it said.

Paul Watters, head of motoring policy for the AA, said the figures were disappointing. "Traffic increases and the weather can be partly to blame, and we hope this is no more than a temporary blip to the long-term progress the UK is making in reducing road deaths and injuries," he said.