Dysonsphere
you are only on an anticoagulant because of an ongoing risk of a further clot or because your current clot is still there. so you cant fly at this stage and comments about different anticoagulants are irrelevant. Factor 10 antagonists are not approved for this condition in any case.
Your specialist will likely investigate why you are getting this problem. There are other treatments available but in most cases the vein 'settles down' and you are then taken off the warfarin. You will have an increased risk of further DVTs but would be expected to live a normal life and merely need to take extra precautions when undergoing operations or flying as a passenger.
So there is really no medical reason you cant fly. Of course that is a medical answer and totally unrelated to Gatwickland........