Low hot water flow in bathroom?

I have just revamped my daughters bathroom and the water supply to the bath and wash basin have been piped in 15mm plastic to each tap from the original supply pipe which was 22mm copper. The length of this 15mm pipe is only the length of the bath less than 2m. The wash basin is still 15mm with the final 30cm in 10mm flexible. The bath tap is now a mixer with 15mm connections and the wash basin is a mixer with 10mm connections. The hot water flow to each is very poor with the wash basin being only a trickle. The shower is electric and independent. I am considering insatlling a pump. Any other suggestions?