I don't think that the Harrier (or any of our fast-jets) has TCAS.
The MoD were forced into fitting TCAS to the AT/AAR fleet when Germany specified that the exemption for Military Transport Type Aircraft (MTTA) would cease from 1 Jan 05. After that date MoD owned MTTA would not have been able to fly in German airspace. I suppose that Nimrod was classified as a Reconnaissance aircraft and retained the state exemption.
It is telling that foreign legislation was required before the MoD would find the money to act. They wouldn't even heed the horrific lesson learned by 2 of our closest allies when a GAF Tu-154 collided with a USAF C-141 off West Africa, prompting both those nations to forsake their exemptions.