I ended up looking at Meest UK uk.meest.com/services/international/delivery-to-ukraine. Their page for deliveries to Ukraine is actually quite useful. They send parcels by both road and air transport and can deliver them to the recipient’s address in Ukraine.

The calculator was probably the most useful part for me, as I could get an estimate based on the parcel details. There are also instructions about preparing the shipment and the information that needs to be provided, so you can sort things out before handing the parcel over.

I haven’t had to use the service for anything complicated, but for a normal UK-to-Ukraine parcel it looks like a sensible option. I’d definitely check their conditions and calculate the price before booking anything.