If the imported garments from Pakistan and Turkey are released to free circulation in the UK claiming preference under GSP (Pakistan) and UK-Turkey trade agreements then these goods will lose their Pakistani/Turkish preferential status and cannot be exported from UK under preference unless they are further processed in the UK and acquire UK originating status under the relevant trade agreement with the country to which these goods will be exported.
If the imported garments from Pakistan and Turkey are not released to free circulation in the UK but instead they remain unaltered under customs supervision, for example stored in a customs warehouse, they may still be eligible for the EU GSP (Pakistan) and EU-Turkey preference when imported to the EU from UK, subject to EU rules. To remain eligible, goods must meet the conditions of the EU GSP and EU-Turkey non-alteration (non-manipulation) rule and be accompanied by a valid EU GSP and EU-Turkey proof of origin made out by the exporter in the GSP country (Pakistan) and Turkey. The goods must not enter free circulation in the UK. As these goods will be imported to the EU through UK, the EU importer will need to check the relevant specific requirements as set out in the EU GSP (Pakistan) and EU-Turkey trade agreements: specifically the requirements relating to direct transport, non-alteration (non-manipulation) and splitting of consignments.
You can find detailed guidance on EU GSP here:
Generalised Scheme of Preferences (GSP)
A Guide for users on GSP rules of origin
You can find detailed guidance on EU-Turkey preference here:
Turkey : Customs Unions and preferential arrangements
We can not comment on the specific content of the EU guidance.