Yes, you can travel without carseats on a one off journey such as taxis etc. A bit like travelling on buses . Don't put the child on your knee then use the seatbelt. If possible they're safer on the seat not on your knee.
I haven't travelled with Addison Lee but have often travelled in taxis with DC on knee. There was a thread elsewhere where a lady whose husband is a black cabbie said this is legal.
I thought AL always used Galaxy's, some of these have a special baby seat built into the row 3 seats. We used one for DC 3 last summer, the back middle portion of the seat pulled forward to reveal a booster and a 5 point belt.
I've just had a quote to Luton airport with Addison lee who have confirmed they no longer supply child seats but are insured to allow us to carry our babies on our laps at our risk. Has anyone had experience of this. It sounds odd considering the general laws around child seats.