An overview of the significant role which BAE Systems plays in the F-35 program is provided by the company on their website.
https://www.baesystems.com/en-us/product/f-35#
The following graphic above provides a representation of this role with regard to the air system.
And the graphic below provides a representation of the key role which the company is playing in integration of the F-35 with the new UK carrier.
There is a webpage as well which provides an overview on the BAE Systems role with regard to F-35 and carrier integration.