The Home Office does not hold these data centrally. Data on 999 response times for the police may be held by individual police forces.
Similarly, the Home Office does not hold data on response times for other 999 emergency services. NHS England publish monthly performance statistics, which include ambulance response times. These can be found here: https://www.england.nhs.uk/statistics/2015/10/08/combined-performance-summary-august-2015/
DCLG publish statistics on fire incident response times, which can be found here: https://www.gov.uk/government/collections/fire-incidents-response-times