Hi There,
Welcome to the site, hopefully we will be able to guide you trough this proccess to be able to see your children.
How old are they?
If you go to a solicitor, they will probably write to the mother of your children asking for contact to be resumed/started, I would have thought that writting the letters alone wouldn't be too expensive, if she doesn't reply or denies access they will probably suggest mediation or court to try and reach a reselution. when you move to court a solicitors cost will start to mount up as they will charge by the hour and one court appearence alone could be as much as £700-£800
I would actually recomend writting the letter yourself and sending it recorded delivery, suggest in the letter that you would like to open discussions to try to re start contact and that you are happy to do this one on one or in mediation if she would prefer, I would want to express to your ex that I would be happy to take things at your childrens pace, and acknowledge that there has been a long break since seeing them and that it will take some adjustments in thier lives, I wouldn't talk about the reasons as to why you haven't seen them only talk about how it can be resolved, keep blame out of the letter and keep things very proffesional. Within the letter ensure you mention that you have given the idea of having to go to court for a contact order consideration and that if needed you will follow this proccess but that you would rather do things personally without using court. Be sure that mentioning court isn't done in a way that sounds as though it's a threat though.
If you can't agree and resolve things then court may be the only option and you can represent yourself throughout this proccess, (we can guide you through so don't worry) there is a guide on how to apply for a contact order and how to represent yourself at the top of the legal section, it wouldn't hurt to have a read to see whats involved.
Hope you can get things sorted, if you need any further info just ask, feel free to share your circumstances as to how contact stopped as it may help with advice.
One last thing when you start to talk to your ex, keep ALL emails, txt and letters as they mey be useful for future reference and could be used if needed if you have to go to court.