No there is no such thing as a common law wife.
As for the policy, without seeing it, it is difficult to tell since different policies operate differently. More usually they go to the surviving spouse, however, they can be written in trust for other beneficiaries or given to trustees with a discretion. You MAY get some, but unlikely and no, you can't contest it.
If your mother has made a will disinheriting you, you are not automatically entitled to anything. We have complete testamentary freedom in this country and if your mother decides to leave you out of her will, then she may do so. If she has no will, her estate will pass under the intestacy provisions under which you may inherit depending on the value of the estate.
You could after death, make a claim under the INheritance (Provision for Family and Dependants) Act 1975, although it is extremely difficult for an adult child of working age who has maintained financial independence to succeed on one of these.