jameswhit If your consumer unit (CU) is fully populated and you want to add another circuit, then another CU is needed. This can be fed from a Henley Block between the supplier meter and the existing CU, or you can have a rethink of your needs and consider either replacing the CU with a larger one, or adding a new smaller CU for additional circuits. You don't say if you already have a Givenergy inverter or how your plant is connected.
If you do have to make changes to your wiring to cater for an EV point, you might want to consider some opportunities: you could break out your lighting, boiler electrical feed and maybe a supply for broadband router etc onto a separate CU which could be fed from a changeover switch from your inverter EPS. This would give you lighting, heating (assuming oil or gas boiler) and broadband during a power cut. This CU could be fed from an MCB/RCBO within your existing CU (or the Henley Block) via the changeover switch. Moving these supplies to a new EPS/Grid-fed CU should make room in your main CU for the EV point and maybe give you some spare capacity.
Don't forget that when installing an EV supply, it's good practice to also install a surge suppressor which will also take up space in your CU.