The first link (page 4) has the last entry:
{"date":"2021-06-04","areaName":"Cheshire West and Chester","areaType":"ltla","areaCode":"E06000050","cases":null,"deaths":0,"pcrPercentage":2.1}
But the first entry for the second link (page 5) is:
{"date":"2021-06-04","areaName":"Cheshire West and Chester","areaType":"ltla","areaCode":"E06000050","cases":52,"deaths":null,"pcrPercentage":null}
So the same date and area, but the metrics are split across the pages, with nulls where they are not included.
Some API v1 results can be split across pages. See this example:
https://api.coronavirus.data.gov.uk/v1/data?page=4&filters=areaType%3Dltla&structure=%7B%22date%22%3A%22date%22%2C%22areaName%22%3A%22areaName%22%2C%22areaType%22%3A%22areaType%22%2C%22areaCode%22%3A%22areaCode%22%2C%22cases%22%3A%22newCasesBySpecimenDate%22%2C%22deaths%22%3A%22newDeaths28DaysByDeathDate%22%2C%22pcrPercentage%22%3A%22uniqueCasePositivityBySpecimenDateRollingSum%22%7D
https://api.coronavirus.data.gov.uk/v1/data?page=5&filters=areaType%3Dltla&structure=%7B%22date%22%3A%22date%22%2C%22areaName%22%3A%22areaName%22%2C%22areaType%22%3A%22areaType%22%2C%22areaCode%22%3A%22areaCode%22%2C%22cases%22%3A%22newCasesBySpecimenDate%22%2C%22deaths%22%3A%22newDeaths28DaysByDeathDate%22%2C%22pcrPercentage%22%3A%22uniqueCasePositivityBySpecimenDateRollingSum%22%7D
The first link (page 4) has the last entry: {"date":"2021-06-04","areaName":"Cheshire West and Chester","areaType":"ltla","areaCode":"E06000050","cases":null,"deaths":0,"pcrPercentage":2.1}
But the first entry for the second link (page 5) is: {"date":"2021-06-04","areaName":"Cheshire West and Chester","areaType":"ltla","areaCode":"E06000050","cases":52,"deaths":null,"pcrPercentage":null}
So the same date and area, but the metrics are split across the pages, with nulls where they are not included.