That doesn't seem to be a weed, but your lawn is greyish brown in parts. First, check the sharpness of the blade/s on your mower, and either get them sharpened or replaced - it looks as if the grass hasn't been cut cleanly, with chewed up, wispy ends. That might be the only problem, because from picture No. 1, I'm not seeing anything other than dead areas at the top of the blades - the grass appears green beneath.If there is another problem, it may be an infection in the grass, but cut it with sharp blades and see what it looks like and how it grows after that.

Second, what routine maintenance do you carry out, if any? I mean things like fertilizing or aerating or scarifying? What's your soil like - heavy and clay or light and sandy?

I'm in agreement with Bamboo - it looks like dead grass to me.

When was your grass last cut?

Thanks for your comments. The grass has not been cut this year yet but has been de-thatched, with a Mantis de-thatcher attachment. I took out two car loads of thatch.
I will be aerating it this week for the first time this year.

The soil is largely clay, with a lot of builders rubble underneath, as I discovered when planting a tree.

The problem seems to get worse each year, it's less visible when the grass starts growing. I will get the mower blades sharpened and see if that makes a difference, thanks for the advice.

If its recently been de-thatched, that usually makes it look worse afterwards for a while. If sharpening the mower blades doesn't make any difference over time, come back and revive your question with that information and more images, or ask another question. Ensure the blades continue to be sharp over time.