The UK ATC system can be a bit idiosyncratic if you are buzzing along at the lower levels and you could end up being inside and outside of controlled airspace at regular intervals.
For those sectors outside of CAS you will get the 'what service do you require' question. It is a UK thing. As Biggin (and Farnborough for that matter) are outisde of CAS you will eventually get this sort of response, albeit for the last few miles of approach at Biggin.
As far as Biggin is concerned, yes we only have one IFR approach to Rwy 21 (working on plans for the other end). So with one published approach expect a visual manoeuvre if runway 03 is in use. Cloudbase permitting.
Sounds like Thames dropped the ball a bit if they vectored you through the ILS and back on from the other side and above the approach. At least they offered a re-vector if you required.
If you are still at Biggin I am back in the office tomorrow (8/4/11) for more formative face to face comment.
Regards
Manager ATS Biggin
Edit: Oh you are in Peru? Forget the latter comment.