This is the tale of Muriel Lester, once famous pacifist and social reformer, and Nellie Dowell, her invisible friend. Nellie Dowell is invisible in the sense that Claire Tomalin described Nelly Ternan in The Invisible Woman. While Ternan, the mistress of Charles Dickens, simply ‘vanished into thin air’, Nellie Dowell, who may or may not have been the mistress of Muriel, trod so lightly on the ground that she left barely a footprint behind her.

Muriel Lester, the daughter of a Baptist shipbuilder with progressive ideas, has been the subject of several books already, including Vera Brittain’s The Rebel Passion: A Short History of Some Pioneer Peacemakers. Born in 1885, she was memorably described by Caroline Moorehead, in Troublesome People: Enemies of War, 1916–1986, as a ‘scatty woman with wispy fair hair wound in Catherine wheels over her ears and rather long teeth’. Fashionably unorthodox, Muriel attached herself to the Tolstoyan cult of the simple life and can be seen in photographs wearing sackcloth and a beatific smile.

There are no such photographs of Nellie who was, according to Muriel, ‘the salt of the earth’. This is effectively all we know of her character. Born in the East End in 1876, Nellie was placed in an orphanage aged nine after which she became that iconic Victorian figure: a little match girl. One of the differences between the two women, says Seth Koven, is that ‘Muriel had a childhood and Nellie didn’t.’ Another difference is that Muriel, who lived until 1968, experienced old age while Nellie, who died in 1923, did not.

Koven, of Rutger’s University, stumbled on Nellie Dowell by accident. Among Muriel Lester’s papers he found 11 letters from ‘Nell’ and two fragmentary documents, written by Muriel, containing some biographical details of her friend’s life. Using these scraps as a starting point Koven tries to fill out the picture, tracing Nelly to New Zealand and Sweden where she was shipped by the match company R. Bell & Co to work in its newly opened factories. The match industry, he writes, was ‘one of the most politicised, female-dominated’ and ‘class-conscious’ in Victorian Britain — it gave the language the word ‘strike’ — but there is no evidence that Nellie was involved in workers’ disputes. She appears to have been content with her rung on the ladder.

How much is it possible to not know about someoneand still write their biography? Koven knows neither when nor how Muriel met Nellie, but at some point in the first decade of 1900 they became what Nellie called ‘loving mates’. What that phrase might mean remains open to interpretation, and beyond noting that middle-class women like Muriel tended to romanticise working-class women like Nellie, Koven does not draw conclusions. We might see them as a version of the ‘Boston marriage’, then a voguish domestic arrangement between bohemian women. Both radical Christians, they read the Sermon on the Mount as a manual of social justice and Nellie became involved in Muriel’s dream of building a ‘New Jerusalem’ in the slum borough of Bow.

At the heart of their relationship was the creation of Kingsley Hall. Named after Muriel’s 26-year-old brother who died in 1914, Kingsley Hall was founded 100 years ago, in Feburary 1915, in an abandoned Baptist Chapel. It was, said Muriel, a ‘people’s house’ and an ‘overdue act of justice’. The building incarnated her belief in the Christian life as one of outward action and inward contemplation, and Koven describes it as ‘an outpost of pacifism, feminism and socialism committed to social sharing’. Here the residents of Bow came together to worship, study, share food and partake in ‘joy nights’, as their moments of enforced relaxation were optimistically named.

No matter how hard she tried to get down with (or go down on) the people, Muriel never succeeded in shedding her persona of Lady Bountiful. In its various guises, Kingsley Hall contains a radical history of the century: used as a soup kitchen in the first world war, it was associated with the suffragettes in the1920s, Gandhi stayed there for six months in 1931, and in 1960 it was taken over by the psychologist R.D. Laing for his work with schizophrenics.

The Match Girl and the Heiress is a mighty odd book, and readers seduced by its romantic title may find themselves surprised. Despite his attempts to bring Nellie Dowell into focus, Koven’s real aim is, as he puts it, to ‘reclaim pre-second world war Britain for Christianity’. The result is a windy 436 pages in which we are given a tour of ‘class relations, gender formation, same-sex desire and ethical subjectivity: war, pacifism and Christian revolution’. Koven’s prose struggles beneath the weight of this burden. ‘It is fair to say’, goes one sentence, ‘that Nellie had received a remarkable if unintended education in the political economy of late-industrial global capitalism as a Cockney subaltern in East London and New Zealand.’

He takes a similarly cloth-eared approach to Nellie’s fragile missives. Described as ‘expressions of love and a form of labour’, Koven explains that they are ‘also objects, literally ink on paper’. Nellie’s untutored prose — ‘I think now the nights are drawing in more will come Kingsley Hall’ — is emptily compared to Gertrude Stein’s experiments in modernism: ‘I went often to see you and every day I said I love you better I do love you better. That’s it.’ Koven finds in Nellie’s omission of a full-stop a mode of ‘literary production … partially shaped by a visual spatial relationship of words on the page rather than the regulatory abstractions of formal grammar.’ If Nellie describes brushing Muriel’s hair as ‘a pleasure I don’t often get and sleeping in your room and keeping you awake to talk to me’, she invokes for Koven ‘tropes of exchange, debt and delight’.

Thus Koven, breaking a butterfly upon a wheel, becomes as obscure and unreadable as Gertrude Stein herself. And poor Nellie Dowell, shrouded in tropes and speculation, remains invisible.