If he's unwilling to accept that your marriage is over, it may be that a couple of sessions of couples counselling will be sufficient to enable you to reach an amicable resolution of child care arrangements and agreement as to the division of joint marital assets.
If this can be achieved, either of you could then proceed to divorce online citing unreasonable behaviour* immediately or you could agree to live separately and divorce by mutual consent in 2 years' time, albeit the current court fees of £415 may have increased. www.gov.uk/divorce/overview
*Unreasonable behaviour does not have to be extreme as the courts generally accept that the fact the petition to divorce is before them indicates that the marriage has broken down and that reconciliation is not an option, nor is the spouse who is accused penalised in any way for their alleged unreasonableness.
It's only necessary to cite 3 or 4 examples of the behaviour complained of which could include spending too much time working, being moody or argumentative, failing to engage in conversations about necesaary household purchases, reluctance to particpate in family events, socialising with others to the detriment of family life, and the lack of intimacy you've mentioned.
As you'd have nothing to lose if he divorced you, it may be this could be an option which tips his scales in favour of ending your marriage sooner rather than later.