You asked

We would like to request statistical information available on the Turkish ethnic group in the UK.

We said

There are a number of tables from the 2011 Census relating to the Turkish ethnic group/Turkish passport holders/country of birth being Turkey/main language as Turkish.
They are available from the Nomis website (https://www.nomisweb.co.uk/).

You can access these from the 'Nomis Table Finder': https://www.nomisweb.co.uk/census/2011/data_finder or the '2011 Census Data on Nomis' page: https://www.nomisweb.co.uk/census/2011

Some of the tables you might be interested in are listed below:

Ethnic Group tables:
QS211EW Ethnic group (detailed)
CT0010 Ethnic group (write-in responses)
Country of Birth tables:
QS203EW Country of birth (detailed)
DC6208EWr Economic activity by country of birth by sex by age (regional)
Passports Held tables:
QS212EW Passports held
DC6209EWr Economic activity by passports held by sex by age (regional)
Main language tables:
QS204EW Main language (detailed)

You may be able to commission a bespoke (more specific to your inquiry) table of 2011 Census data. Census Customer Services (see below) will be able to advise you on the procedure and the associated costs: https://www.ons.gov.uk/census/2001censusandearlier/dataandproducts/dataandproductcatalogue/commissionedoutput

If you have any further census related questions may I suggest that, rather than using the Freedom of Information route, you contact Census Customer Services directly.
Web: https://www.ons.gov.uk/census/censuscustomerservices
Email: census.customerservices@ons.gov.uk
Tel: +44 (0)1329 444972
Census Customer Services: ONS, Titchfield, Fareham, Hants, PO15 5RR

It may be possible for you to obtain the information you requested specifically relating to employment/unemployment from the customer services team of ONS Social Survey Division. Special extracts and tabulations of Labour Force Survey (LFS) and Annual Population Survey (APS) data are available to order (subject to legal frameworks, disclosure control, resources and agreements of costs, where appropriate). Please contact socialsurveys@ons.gov.uk or use the weblinks on the 'requesting statistics' page: https://www.ons.gov.uk/aboutus/whatwedo/statistics/requestingstatistics