An initial consultation is just that - a chat to see if you wish to engage the solicitor, and if they wish to take your instructions.
It is standard for a solicitor to write to you and confirm that they are acting on your behalf - this starts the formal relationship.
If you have not engaged the solicitor - your choice - then you are not classed as a client.
You cannot refer to the solicitor as 'your solicitor', but you are free to say you have consulted 'a' solicitor, as long as you do not name them in a legal context - to a court, or another solicitor.
The advice the solicitor gave can only be based on the information you have shared with them - they are not mind readers, so cannot advise you on facts which may be relevant in a court case, but which you have chosen not to share with them.
If you have not gone beyond the initial free consultation, then you cannot claim to have been advised by any of the solicitors you have spoken to on that basis.
Solicitors' initial consultations are free - as a fact-finding exercise to see of they are suitable for you - not all solicitors deal in all aspects of law, and some specialise in certain areas.
A solicitor's advice is not free - so if you engage their services, and they will write to confirm that you have done so, then you are legally bound to pay for their advice and services, but that does make them 'your' solicitor who has advised you.
Hope this helps.