OP, I'm a will writer, and strongly recommend that you do make wills.
At present, because you aren't married, you would not receive anything, as your home is in your partner's sole name. If he dies before you, his estate will go to his children in trust until they're 18. That will involve your being homeless (I presume that the capital you used to help with his mortgage was all you had? - did you do a deed of trust?). What will happen to his daughter if her mum has no contact? Unless he appoints you guardian she will probably go into care. The guardianship issue is a bit tricky, as technically her mum would automatically be expected to care for her, but in these circs, as there is no contact between the child and mum, making a guardianship appointment would probably be adequate to ensure that she didn't go into care.
There's also the issue of the interest you may have acquired in his house by making the lump sum. This needs to be sorted out properly. It may be appropriate, given that you have children both in your relationship and the elder children, for your partner to, at the very least, give you a right to reside in the house for a specified period, or (preferably), either a life interest, which means that you can stay there till you die or marry someone else, or a gift of part of the house. By making a life interest, he can still protect all or part of the house for all of his children but still give you the security of a roof over your head. Here's an article about life interest trusts: www.marlowwills.co.uk/protecting-your-estate-from-care-home-fees.aspx
which explains how they work in blended families (ignore the care home fees title, that's the other use of this type of trust).
So far as charges go, will writers are generally cheaper than solicitors as they often work from home so don't have the overheads of a high street firm. You should ensure that you use a member of the Institute of Professional Willwriters who are all properly qualified, regulated and insured. High street lawyers (I was one for many years), charge quite a bit more, depending on where in the country you are.
Whoever you choose to make your will, I suggest that you get on with it sooner rather than later. Once it's done, you can tick it off the list of Things To Do When I'm A Grownup 