My husband and I had counselling for fertility issues and also Christian counselling for issues because of the fertility. It was very helpful.
I don't know what is available to you locally and I guess Relate is a place to start.
I think one issue is really do you love each other or did you once, can you regain that love.
I think it is good to try to build your relationship up or to re-build it a new, not for the sake of your son but for yourselves, if you can build it up as new thing and love each other that would be great.
I sense you may both have your own motives for staying which are not about love, perhaps in a good light about support for each other of for simply getting the support you each need.
If you do go for counselling go into it with as much of an open mind and heart as you can. Be prepared to look at things in a new way and see a new way ahead.
If there is no abuse and he is basically a good guy who you argue with a lot there may be a way to move forward. If it is in any way a dangerous or risky situation for either of you then I would not want to stay.
Agree with Lweji when they say I don't think anyone can advise on what is the best counsellour. I think you should "interview" a small number and go for the one that both of you are happiest with.
And you say If the counselling shows us that there's no way forward together, I'm also viewing it as a way to help us manage the breakup, financial separation, custody etc, and to co-parent DS amicably. I agree, it can only help.
Good luck.