No, but it does run near Mildmay Park.
Of the six, this is probably the least geographically accurate (as mentioned) and possibly the least relevant.
The hospital of that name has never been anywhere near Mildmay Park. It took its name from that area because its work was originally set up by the vicar of St Jude's Church and his wife, the church being located in Mildmay Park. This is not an open space but is a thoroughfare stretching from Newington Green to Ball's pond Road. The road, together with the church, was built in the 1840s when part of the Mildmay Estate was leased for housing at the time the North London Railway was under construction. The "Mildmay Mission", which the work of the church became known as, opened its first medical centre during a cholera outbreak in the East London slums. This was located in Bethnal Green, near to the current Mildmay Hospital.
It is probable that only people who live in that immediate area know of Mildmay Park and not many of them would be aware that the building which sat on the railway bridge crossing the "Windrush" and "Mildmay" lines was in fact Mildmay Park station, which closed in 1934. Some may have known it as John Holton's vehicle body repair shop, which operated from the substantial former station building from the late 1950s until shortly before it was demolished in the early 1980s. Whilst it's said upthread that few people will have heard of Mildmay Park I would fancy that not many more have ever heard of the hospital.
I feel insufficient thought went into the naming of the Mildmay Line. It seems to me that whoever conducted this exercise saw the hospital and decided to fit one of the six lines to it, come what may. Their cause may have been better served if they'd at least chosen one of the two lines which pass close by.
...and that Windrush actually rushes through Brixton without stopping.
To be pedantic it doesn't actually rush through, but more glides over on the girder bridge which crosses the platforms at Brixton Station. Despite being immediately above the platforms which serve the trains to Herne Hill and beyond, there are no platforms on the bridge which takes the tracks towards Denmark Hill.
..one person gets it! The level of historical ignorance and confusion on this thread is shocking.
The only one which makes any sense is the 'Weaver' Line which has a nod to the historic industry in that area.
The ignorance is not really that shocking. I imagine few Londoners - especially recent arrivals - can tell you much about the Huguenots and I imagine even fewer know very much about their weaving activities. In fact, the BBC article on the lines' names says this about the Weaver Line:
"With stops including Liverpool Street, Spitalfields, Bethnal Green and Hackney, the route travels through several areas of London known for their importance in the textile trade."
Whilst TfL's own article on the reasoning behind the names certainly mention's London's weaving industry, the BBC seems a little light on their history. Leaving aside there is no station by the name of Spitalfields, the link from that description makes no mention of weaving at all but concentrates entirely on garment making and the fashion industry. This is unsurprising because I believe the weaving industry in London's East End began to decline in the early 1800s and was all but finished soon after the middle of that century. I don't believe there has been much "weaving" taking place in that part of London ever since.
Of course the fashion trade and garment making in particular flourished in the East End and particularly along the route of the Weaver Line between Bethnal Green, Hackney and Dalston. Many immigrant populations were prominent in that trade, especially Jewish people, but also Irish and more recently, Bangladeshis, who brought their garment making skills to London. I suppose the "Rag Trade" line doesn't carry quite the same gravitas!
