Grass type weeds in the lawn

My lawn has several patches of a grass type weed in the lawn. Not sure if its crabgrass, perennial ryegrass or Yorkshire fog, but I find it annoying especially as it has now spread to several areas. How can I get rid of it? Am I best digging up the lawn in these areas and re-seeding? I guess normal lawn weedkiller won't work as being grass it will shrug it off. The largest patch is about 18 inches by 12 inches.
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Here's a picture of the offending grass, if anybody can offer any suggestions. I did read that if you run a sharp knife thru' it in a criss-cross to cut the roots up that will weaken it, but not sure how effective it is. Anybody offer any helpful solutions? Do I just need to dig it out to bare earth and re-seed?
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
I’ve read there is a herbicide called rescue that green keepers use but it’s very expensive