As
@Cagey75 says the X-T1 is probably the way to go, for general purpose and wildlife options (within your budget). The big difference between this and other Fuji X-Trans1 and 2 sensor offerings is the EVF, its big bright and just lovely to use. S/H this will eat £400 of your budget. The X-T1 also has some zone focus and tracking options.
Regarding lenses you have £600 left to play with, this gives lots of options, and it really depends if you want any wide aperture lenses in the mix. Besides the 55-200 there is a lower cost 50-230 zoom, its plastic bodied, still optically good, but doesn't open as wide, but its available in Mk1 form for £100-£130
Possible Options are:-
1) @Cagey's suggestion 55-200 + 35mm F2 - going to be just about on budget
2) 18-55mm + 55-200mm - just over budget (£650 ish), don't think of 18-55mm as a kit lens it really is rather good
3) 18-55mm + 50-230mm - under budget at around £375, you could probably squeeze in a 35mm prime as well and be about on budget
and lots of other combinations!!
Or just get X-T1 + 18-55mm, have a play to see if you like the Fuji system then invest in the 100-400 when funds permit.