Sorry to hear you may have to go through the process pal, it's a minefield. Took me a few (stressful) years but got there in the end.
Some solicitors will give you a sit down meeting for an hour or two, get all the facts and your side and then write a letter to your ex outlining when you want to see them etc. and asking for agreement without the need for legal action. They do this within a fixed fee (I think I paid £200 three years ago). I used Rutherfords in Tamworth.
If she's not on board, your next port of call is mediation which is mandatory. You don't need to arrange that via a solicitor, you can do it all yourself. She has to attend, if not the courts will take issue with her if/when you issue proceedings for access. Mediation is not too expensive, about £60 for a few sessions between you. Or free for both if she's entitled to it (e.g. doesn't work, receives tax credits etc.) The mediator will meet with you separately and then jointly and draw up an access plan. It's not binding, but if she doesn't stick to it again the courts don't look fondly on it. The courts can make it binding if you get that far.
If she doesn't get on board after all the above then your option is to issue proceedings. Again, you don't need a solicitor, you can do it all yourself and represent yourself. It's not complicated if you read up first. The issue fee is around £200 only, it's the solicitors fees that cost a bomb. In most cases, the courts will award you reasonable contact after a few hearings over a couple of months and she will be bound by that.
The caveat to the above is if she is making domestic/drug/alcohol allegations against you. In those instances it is more complicated and take longer, but you'll still get there. Mine was the above route but a family member was accused of beating his ex by her and being addicted to cocaine etc. (Complete fantasy) and it took him a year of fighting in the courts but he now has his two children from Friday to Sunday twice a month as ordered by the court.
Bottom line mate, it will all come good. The courts attitude has changed a bit of late, women no longer get free legal aid and in the majority of cases men do get their access unless there is a criminal record for violence against the ex and kids.
PM me if you want any advice. Good luck with it all