"Centile", not "percentile": the UK's own terminology
UK health visitors and the red book universally use the word "centile" rather than "percentile" for exactly the same concept, so a UK parent reading an American growth chart described in "percentiles" is reading the same measure under a different name. The 0-4 years UK-WHO growth chart used in the red book blends WHO international standards with UK-specific data.
Health visitors watch the trend across centile lines, not one measurement
UK guidance focuses on whether a child's growth crosses more than roughly 2 major centile lines on the chart between checks, either up or down, rather than which single centile they happen to sit on at any one visit, since a steady line is usually more reassuring than a single high or low measurement in isolation.