The value of Research and Development (R&D) tax credits and the number of businesses taking those up for the years 2000-01 to 2016-17 are published in the relevant National Statistics:
The same publication contains the number and value of claims for Yorkshire and the Humber for 2015-16 and 2016-17. The number and values for earlier years are published in previous publications:
The value of tax credits and the number of businesses taking up tax credits by county or unitary authority for 2015-16 and 2016-17 are published in the supplementary tables. Data for other years and geographies would only be available at disproportionate cost.
All these tables are based on registered office location, which may not be where the actual R&D activity is carried out.