How can I erradicate wild garlic in our garden which has snowdrops, daffodils and primroses scattered amongst the weed.

Highly unlikely you will succeed. You could try a removing the individual bulbs but there will be a huge number of bulbels.

The only way is to dig them all out, every other method I've tried has failed. I go through every spade full of mud and pick out each bulb with my bare hands - not fun.

That's the way I did it too madmum. A long task but worthwhile in the long run

You obviously won the battle in the end Andrew, you give us all hope! I'll be returning to battle with the evil alliums as soon as the weather improves :(

I have removed much of the same in 6 months.
First take out all the snowdrops, primroses and daffodils. Plant them in another place. Weedkill the whole area with sodium chlorate, this is a total weedkiller which will kill everything. In 6 months time (September) the salts from the weedkiller will be neutralised and grass etc. will grow again, but not the wild garlic.

I think sodium chlorate is now banned Doctorbob1

No It's OK, I bought some in Wilkinsons at Xmas, for getting rid of a treestump. Also it is on Amazon even. I think there may be restrictions on it in some areas and it is explosive and highly inflammable.