Get legal advice as soon as possible on formalising access to your son. You do not have to be divorced for this to happen.
If your marriage has broken down, but you have a Court order for residence or contact with your son, then you may qualify to stay under
Paragraph 248A of the Immigration Rules.
Requirements for leave to remain in the United Kingdom as a person exercising rights of access to a child resident in the United Kingdom
248A. The requirements to be met by a person seeking leave to remain in the United Kingdom to exercise access rights to a child resident in the United Kingdom are that:
(i) the applicant is the parent of a child who is resident in the United Kingdom; and
(ii) the parent or carer with whom the child permanently resides is resident in the United Kingdom; and
(iii) the applicant produces evidence that he has access rights to the child in the form of:
(a) a Residence Order or a Contact Order granted by a Court in the United Kingdom; or
(b) a certificate issued by a district judge confirming the applicant's intention to maintain contact with the child; or
(c) a statement from the child's other parent (or, if contact is supervised, from the supervisor) that the applicant is maintaining contact with the child; and
(iv) the applicant takes and intends to continue to take an active role in the child's upbringing; and
(v) the child visits or stays with the applicant on a frequent and regular basis and the applicant intends this to continue; and
(vi) the child is under the age of 18; and
(vii) the applicant has limited leave to remain in the United Kingdom as the spouse, civil partner, unmarried partner or same-sex partner of a person present and settled in the United Kingdom who is the other parent of the child; and
(viii) the applicant has not remained in breach of the immigration laws; and
(ix) there will be adequate accommodation for the applicant and any dependants without recourse to public funds in accommodation which the applicant owns or occupies exclusively; and
(x) the applicant will be able to maintain himself and any dependants adequately without recourse to public funds.
It is important to maintain contact with your son, and it sounds as though you will need legal assistance to do this.
There are other threads about people who have used this route to stay: search the forums and you will find people who have been in a similar situation to yours.
