A small Bee like creature leaving several small mound like holes in lawn we are talking about 20 in a small lawn, patches of yellow grass now appearing worried that they are killing my lawn!

This sounds like the activity of either the Field Digger Wasp or the Slender-bodied digger Wasp. They make burrows in the soil, paralyse a fly then place the fly and an egg inside the burrow. If your soil is relatively sandy or very light, this is what you have. I doubt whether their activities would cause yellowing of the grass, unless your lawn is totally infested. It could just be drought.
As to getting rid of them, you could try Derris dust puffed or sprinkled into the individual burrows. That's all that comes to mind, at present. The drastic measures employed to eradicate colonies of Common Wasps would be inappropriate, as Digger Wasps are solitary.
Bbb

If it looks like a bee, (fuzzy) then it likely is. I suspect that it is the mining Bee Andrena haemerrhoa. They leave little volcano-like mounds especially in loose friable soils that are easy to dig. They won't damage your lawn so just leave alone and being solitary, when the young emerge, they just go away and don't re-use the same hole.

Just to say all bees (and wasps too) act as pollinating insects and with the problems facing honey bees we shouldn't be doing anything to harm our other pollinators. No bees are harmful and wasps are just a nuisance, but do lots of good taking pests too.

i agree bertie id be inclined to get a microscope lay close to a hole and study what they do.the spiders you get with a large abdomin at the end of summer can definatly tell bye touch what has landed for dinner in there web.if its a blue bottly they run strate to it and bight.if its an earwig there a bit more carefull and rap it up first.if its a wasp there amazingly carefull and a human finger they just run of.i dont think this is site as it takes a little while to register ie feal.quite amazing realy.

I also completely agree with Bertie too.