Air works, not BAe, and no, they repaired them using F2 fuselage sections.
The major reason was the end of the Cold War and subsequent defence reviews which eliminated the Germany and Wattisham based F4s (in the CR role as a dogfighter against Mig 29s) and the Jaguar fleets which the Eurofighter was planned to replace. In order to preserve industrial capability and work share on the Eurofighter programme, and since we were contractually to buy them anyway, the decision was made to use them to replace the UK based long range interceptor F3 fleet instead.