No idea what "Twitch" is im afraid !!!

I think you mean couch grass. I would suggest that you dig it out manually or wait until it starts to grow and use something like Roundup (glyphosphate). I know it will take some time but the couch grass will come back to bite you if you don't get rid of it to begin with.

And it definitely will grow through the turf and being grass there will be nothing you can do about it then, except dig up the patch and start again. Been there, got that!

I agree. It's not too bad to dig out, and strangely satisfying to follow each piece back to its origin. I don't think it will be the end of the world if a few bits are left as constant mowing will keep it in check.

Sorry, but our grass has been mown regularly for the last 20 years and the Couch grass is slowly taking over and spreads out into the borders.
Easier said than done to dig it all out too, especially on a heavy type soil.

Our lawn must have been laid with cheap turf as its full of twitch, which does its best to spread out into the borders, but short of returfing we are stuck with it. Regular mowing does little or nothing to discourage it. Even if you spend ages digging out all you can find you're bound to miss some. I'd agree that if you want to clear it all its best to remove what you can, wait a season and glyphosate any new crop of it that appears over the summer.