That’s going to be either
a) pretty expensive if you get it re-turfed or
b) a fair bit of work if you remove it all yourself and re-seed
I would maybe try to embrace your lawn.
Mine is a complete mish-mash. Can easily see where previous owners have re-seeded as grass type varies a lot re growth/thickness etc. I have a fair amount of moss. Lots of clover/clover flowers. Buttercups, daises and dandelions.
I’ve decided that life is too short to try to create a “perfect” lawn. With all of the above, when I mow it, it still looks neat, tidy and green. When it gains a little growth, it is lovely to see lots of bumble bees etc enjoying what’s on offer.
The only things I occasionally dig out are the weeds with spikes on - can’t remember what they’re called. And there’s one patch of lawn where creeping buttercup can run rampant - I usually pull it up by hand once a year and, after that, it seems to keep it under control for the rest of the season.
As an aside, just a pointer to not water your lawn if it’s established. Even when you’ve had lots of warm weather and it looks like straw. Grass is resilient - all the “growth” takes place below surface. It WILL come back lush and green, don’t waste water on it.