Can I Apply for Full Custody

I live in the UK and after divorcing 2 years ago my ex-husband and I have joint custody of our children

I am not happy with the fact that the children regularly come back to me after time with him with dirty clothes, not having been bathed, and smelling of cigarette smoke. I know he smokes in front of them even though time and time again I have asked him not to. One of our children has had breathing problems in the past, but this does not seem to make him stop smoking in front of them.
There are times when they come back to me without having had breaksfast or a meal for hours.
He leaves them with relatives while he goes and spends the night with his girlfriend and when he comes back in the morning this usually means that my children are late for school.

I have asked their father time and time again to stop these ways and take more responsibility, but he does nothing to change.

I am wanting to apply for full custody of my children as I honestly do not feel at all at ease when I know they are with him and I know he is not taking care of them to the best of his ability.

My question is, is it worth going seeing a solicitor about this; in the sense of, are the courts likely to award me full custody, or are they likely to say that the problems mentioned above are not enough to warrant granting me the full custody.

Thank you in advance.

This is a U.S. forum, so we can't help you with a U.K. legal question. Laws can be very different between nations - they differ a lot between U.S. states. Here, I would expect that a court might order some remedial steps (e.g., "no smoking in the presence of the kids", observing standard meal times, possible orders pertaining to who can care for the kids during his visits) rather than a denial of visitation.