As Gill says, 30 Oxford Road seems to have been the Laidler family home - Maria H and her parents were there in 1861 as well as in 1871. This particular Oxford Road seems to be the one now known as Elizabeth Avenue, London N1.
There's a small possibility that Frances's father's name is a (semi-)fiction, and it looks unlikely that you'll be able to find a paper trail to the right Frank (or Francis) Baker, but you can look for possible candidates. Being in the right place at the right time to be Frances's father doesn't prove paternity, but it is a necessary starting point.
A birth mid-way between two censuses doesn't help, but I found two men of the right name who were clerks in London in 1861/71. There may have been others.
Francis Baker b Northover, Ilchester, Somerset. (Q3 1838 Yeovil registration district) was a bank clerk. He and his brother were living as boarders in Camberwell, Surrey in 1861, and he was living with his, by then married, brother in 1871 in Lee, Kent. He had moved with his brother’s household to Stoke Newington, Middx by 1881.
I don't see anything linking his location to Maria's, but I did notice that Frances's stepfather was also a bank clerk living in this part of south London.
Francis Henry Baker b Lambeth, Surrey Q2 1840 is possibly a bit more promising. He was living with his widowed mother on Euston Road at the northern edge of the City of London in 1861, when he was a clerk (/ secretary?). They’d moved to Penge, Surrey by 1871, when he was a clerk.
By 1881, he’d married and was living in Kensington. He now worked in the Civil Service: Inland Revenue, and by 1891 he was a Clerk, Upper Division, Civil Service. In 1901 his occupation was Civil Service: Chief Examiner, and by 1911 he’d retired.
Nothing here is a perfect fit, but it doesn’t look impossible either. His location on Euston Road in 1861 places him a couple of miles from Oxford Road (Elizabeth Avenue), so he and Frances weren't exactly neighbours, but they could have met. Or, of course, they may not have done. And by 1889, he was a married member of the Respectable middle classes who may have preferred Frances’s marriage register didn't directly reveal his occupation / identity.
I'm not sure how much this really adds to what you already know, but you might find by exploring one of these men further that something fits - or that something rules them out.