You and your children will need a visa.
I suggest you visit this website
UK Visas which is an official UK Gov't website.
See the section on "Do I need a visa?" so that you can provide details particular to your situation - as you don't say what nationality you are, I'm not going to assume anything. You
may be eligible to settle if you, your parents or grandparents are/were European citizens.
Generally, you cannot immigrate on the basis of having a boyfriend in the UK. You need to be engaged, married, or have special employment skills. Some of the other members may be able to provide more information based on their experience. I got my settlement visa on the basis of marriage to a British citizen who lived in the UK.