I can't remember where I heard about this, (it might have been here), but one possible path I've heard proposed for a TL with a more successful Babbage and Lovelace is a Victorian proto-internet. Imagine those early machines connected by telegraph, able to communicate via a set standard. You could have finance and industry driven by the rapid tabulation of prices and delivery schedules, increasing efficiency. You could see consumer finance being standardized: A Victorian lady in a department store could make purchases on bank credit, with the store simply sending that data directly to the bank's engines via telegraph, which then calculates the changes to her (or her husband's) account.
Taxes are also something that could be made much easier to calculate and collect here. If someone invents witholding, you could see effective and efficient income taxes in Britain by the 20th century. Other taxes are possible to envision as well--If tax liability is linked to a bank account, a corporation or individual could have excises, sales taxes, or VAT style taxes calculated for them based on data they report in on a regular basis, with this reporting being further telegraphed to tax collectors for reporting and automatic payment from that same bank.
This is infrastructure-intensive until someone discovers how to run multiple signals down a single telephone/telegraph line, but when that occurs you could see an explosion of innovation on the idea.