Joie - elevate™

There's different regulations in the UK for car seats so most/all American seats might not fit. Depending on the area of the UK you are planning to visit you might find public transport is a better option than renting a car and definitely a safer option than renting car seats that you can't guarantee haven't been thrown about and damaged. If you are planning on coming back then you could buy 2 inexpensive seats to use next time there is a joie seat that's both HBB and 5 point harness forward facing to 18kg (the weight limit is the only limit and must not be passed) they are around £40/$52 a seat

That would be a good option, the joie elevate would work for both kids unfortunately at £80 each or for the older one as it's HBB only the joie trillo. If you are getting public transport from the airport I wouldn't worry about buying them until you get to your destination and look for a Halfords who may have some in stock, Amazon or smyths, and look for belt fitted as older cars don't have extra attachment points apart from seatbelts.