Sounds to me like Gatwick were just splitting.
When bandboxed, Gatwick Director is one person, working the frequency you were on. If it's getting busy (as you said it was) then two people will do it - one as intermediate director and one as final director on the other frequency they opened. What probably happened is that one person working was putting them on the ILS then transferring them to the tower, until the second person arrived to split, at which point they would transfer them to the person who was opening up FIN.
Occasionally intermediate director will keep one on his frequency as it's easier, but a Gatwick person would tell you more!
Hope this helps.
Cheers,
N
"Keep smiling, it makes people wonder what you're up to...."