I recently retired from a full-time post at a very senior level working as an Art Psychotherapist in the NHS in the UK (I am an Irish immigrant, by the way). I worked for the NHS for 18 years after an unsuccessful attempt to set up a private practice. What follows is therefore anecdotal and may not be representative but it's my "tuppence'urth".
(1) Pre-recession it required about 3 years to build up a clientele of 15-20; post-recession this is likely to be longer. Affordability is an issue as self-help and public-sector options proliferate. (2) Setting up involves a lot of leg-work, self-publicity, presentations to potential referrers and business-meetings. You mention a web-site but with such a personal, intimate relationship as counselling or psychotherapy recommendation, word-of-mouth from individuals with whom you have worked safely and effectively, and referrals from General Practitioners, are the main source of clients. (3) If/when you establish a clientele, factor in time and energy to keep accounts, maintain secure accurate records (check this out with whichever professional association you trained with/sets your ethical standards........the criteria for security and documentation are extremely rigorous!). (4) Following closely from the previous point, professional training bodies now require that registered practitioners have comprehensive, expensive, third-party liability insurance as well as adequate and appropriate caseload supervision so time, money, energy and availability of the would be a core element of your private therapy practice...........irrespective of the size of your client group.
In summary, working with individuals with troubling personal issues and/or dysfunctional relationships is not to be engaged in lightly and there is no option of 'casual' or 'part-time' involvement. You would like to do 'a little' of this work but the reality is that therapeutic responsibility does not end when the individual leaves the session, but when the therapy is completed which may be a number of years. Given that you are unsure if you wish to emigrate setting up a practice in current economic climate and given the nature of the enterprise would, it seems to me, benefit from you discussing with an experienced mentor/supervisor from your professional body, in your own field, to assist you to decide.