"Are there medical consultants specifically for CFS?"
There should be, but in the NHS there are not. There used to be NHS ME medical clinics in the 70's and 80s, with specialists, not many, but they took referrals. That stopped during the 90's when a kind of land grab took place whereby a group of UK psychiatrists 'claimed' ME, preferred to call it CFS (a name that can be confused with the common symptom of fatigue which is a symptom of many diseases and conditions) ..... they created a new diagnostic criteria which was so wide that just about anyone who experienced tiredness could have it (The Oxford Criteria).
The new criteria created a 40% misdiagnosis rate. That's people who were wrongly and often casually given an ME or CFS diagnosis but who suffered from other (often treatable) conditions including Crohn's disease, Coeliac disease, primary heart conditions, MS, major depression and more, who were left without treatment for their actual disease.
The psychiatrists who had 'claimed' ME asserted that ME (CFS) was merely deconditioning and false beliefs by deluded patients.
So, the Graded Exercise was designed to recondition, the CBT was designed to convince physically sick people that they are not physically sick . This was initially asserted with no research or other evidence whatsoever.
The flagship research (The PACE Trial) which claimed that ME or CFS sufferers 'recovered' by graded exercise and CBT has been exposed as so flawed that it should never have got through peer review, and is described by Carol Monaghan MP as "One of the greatest medical scandals of the 21st century."
So we lost 30 years during which biomedical ME research was not funded in the UK, all public research funding going to CBT GET (graded exercise).
The so called CFS clinics offered CBT/GET and rarely anything more. Some individual therapists in the CFS clinics went against their training due to realizing that the Graded exercise was making their ME sufferer patients more sick, taking them from mobile to bedbound too often.
We could and should have had experienced ME medical specialists in every hospital. We hope that will take place in the future but much of the expertise of the 70's and 80's specialists was not passed on and has been lost.
So the significant research is done outside of the UK. It all needs more funding but there is hope and top medical researchers worldwide are on the case.