Yes, you get an app and you can see the current and historical prices, in 30 minute increments.
Looks like this:
But if you want, you can also export all of the data as an excel spreadsheet.
Some car chargers(OHME for example) can read this data in real time and only start charging when the price per kWh falls below a pre-set level.
They do, they expose it via an API, so you can use IFTTT (or anything you make that's similar to this) to optimise when you use power.
This website does some analysis on the pricing: https://www.energy-stats.uk/octopus-agile/
The useful part is that, if a user of the tariff is sufficiently engaged, not only do they save money, but by shifting their demand to follow supply it helps with the increasing adoption of renewable sources.
https://www.nordpoolgroup.com/Market-data1/#/n2ex/table this is the market price you need to find out the margin + transmission costs yourself.
Does Octopus provide the price of electricity at the current moment?
I had a quick look at their website but couldn't see anything obvious.