I have separated from my partner for 18 months now and she has completely stopped all access to my two wonderful children (2yr and 4 yrs). She demands I pay maintenance which I am sure she spends on herself and not my children. On top of that I have not seen them for 18 months.
Can anyone recommend a cheap family lawyer?
Ex-family lawyer here. It's a bit of a flag that you've not seen your kids for 18 months (i.e. your youngest was 6 months when you last saw him or her and they have not known you for ¾ of their life), and you're only just looking to resolve this now. And it would appear to an outsider that you are only considering your position as a result of demands for maintenance - you mention not seeing your kids as a matter "on top of" the maintenance demands. Time with your kids seems a secondary consideration, given how you put it in your post. Not a great start with regard to any court presentation.
That being said, contact is a right of the child, for the best interests of the children, not a right of the parents. As such, the presumption will be that some form of regular direct or indirect contact with you will be in their best interests, unless there is some other intervening factor (emotional distress, domestic violence etc). This is best done by agreement, but can be done by court order backed with sanctions if ignored. For all kinds of obvious reasons, better it is done by agreement to ensure it works smoothly. Fighting every visit out with your ex will be emotionally and financially draining for you both, particularly if it ends up with frequent court visits, and harmful for the emotional wellbeing of the kids (which can be one reason incidentally to refuse future contact...). Better to use family money on yourselves than on lawyers and mediators.
My advice? Agree the maintenance position ASAP with her first. Don't try to link it to what you perceive to be access rights. Whether or not you have contact with the kids, you are for better or worse financially and morally liable relative to your means. Any maintenance money is for her and kids for kids' benefit. Don't worry about what precisely she spends it on - to some extent it is irrelevant unless she has some financial problem such as a gambling issue: it all goes in the family pot and enables your joint children to be maintained. Agree a reasonable figure that you can afford as a separated family and then stick to paying it.
Then unless she is refusing any and all contact, in which case you will need lawyers, separately agree regular structured contact with her depending on your living circumstances. Could be weekly, fortnightly or whatever. You may well need some introductory sessions with her and the kids at first, or a third party or contact centre (if they still exist), if it has been 18 months since you've seen them and they are potentially unsure around you.
Sorry if that appears blunt: it's not intentional. A degree of that comes from it being on the internet rather than in person - genuinely wish you good luck and hope you get it all sorted without the need for lawyers!