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The Mortgage Indemnity Guarantee Premium is a payment often demanded by a lender in order for them to lend.
It protects the lender from problems should you default on the loan and be repossessed. The insurer will settle with the lender and then come after you for the money.
You might have heard reports that the policies didn't actually work, in that the insurer could not pursue you. This might be the case for some existing policies, but any potential loopholes can be regarded as closed with regard to new policies.
How hard the insurer will press for repayment is open to debate, ( considering that you will have already been repossesed ). The consensus is that they will pursue until convinced that there is no money, and no prospect of money. They might go so far as to bankrupt you.
The premium can vary massively, sometimes from £100 to over £1000 for similar mortgages with different lenders. Ask your mortgage adviser to sort the mortgages on the basis of seeking a small premium.