Short term you could take parental leave to give you time to organise this. If this is a recent breakup and you need some time from the pressure of work, Gp could well sign you off to give you time.
if you have the space, an au pair is probably most cost effective. Babysitters via childcare.co.uk maybe a possibility.
Outside of these options your only real option is to apply for flexible working with more family friendly shifts- you’re entitled to apply once per year. Make sure work know you’re now the primary caregiver.
Longtermi would think if employed with night shifts specified in contract that you’re unlikely to get much movement on this and probably are realistically looking at changing jobs to one with more friendly hours.
Look on your local council website to see what child care provider s are able to assist you. It took me 7;weeks to get child care in place so be warned. The council will have a free list . Do not use these so called childcare website s they are full of strange people who are just running a business plus you will need to pay to correspond with them .
there are childminders who take children overnight…obviously your children would need to spend some time with them etc first. I imagine the cost paying for children to be cared for all night would be high. my child minder used to look after a little girl who’s mum was single and did 12 hour nights as a prison officer. mum would pick her daughter up from school, do tea, play homework bath and pjs. then drive her over on her way to work and pick her up I the morning. she did 3 night shifts? money was better and no real time lost with her daughter. I don’t know how she funded it though. the other option is someone coming to sleep at your house with the children but that would involve a massive amount of trust. is there anyone you know who would be trustworthy, doesn’t have commitments of their own and would appreciate the money? or a family member that would help you (even if it’s your ex partner’s family they may do it for the children)