Is this possible?
Yes, but in reality it’s very very difficult.
What you need is a Consumer Access Device (CAD) that is paired on the Home Area Network (HAN) used by your meters. The HAN uses Zigbee radio, which is easily accessible to the maker community, but any device has to go through the necessary testing and certification before it can be paired on the HAN. This limits options to a commercial device of some sort, of which there aren’t many (any?) yet. There were a couple of options for SMETS1 but none that I know of yet for SMETS2. Even then, the meter readings had to go via the manufacturers cloud service and back to you via their API. There was no peer-to-peer functionality to pull the meter readings directly over your local network.
Even if you manage to purchase a suitable device, Bulb as yet have no way to pair the device for you. It’s something the supplier has to do, you can’t do it yourself. Anecdotal evidence suggests other suppliers aren’t much better with this procedure either, although it should be noted that they are required by their operating license to assist customers with pairing their devices.
Some of the Chameleon In Home Display (IHD) devices installed by Bulb have an option to connect to local WiFi, but as yet it doesn’t appear to do anything. Apparently it’s used only for firmware updates. Perhaps some local API will be implemented later by Chameleon, but I doubt it.
TL;DR: Yes but no.