No, INCOTERMS do not affect the use of a T1. However, your INCOTERM will affect who is responsible for the export customs clearance, which may affect who is responsible for contracting the T1.
To avoid complications, we recommend using the same broker for the export clearance and the T1 so that they are completed at the same time and with the same information. Make sure that all parties are clear on their responsibilities during the contacting for sale of the goods.
Universal Customs Clearance provide T1 transit documents and export clearances from all major UK ports. Contact us for more information.