I think the only thing that is portable for that age group is:
Nachfolger Hy5 (inflatable rear facing seat)
Maxi Cosi Nomad
Urban Kanga
TinySeats
RyRy Scallop
Ride Safer Travel Vest
None of them are ideal.
The Nachfolger has decent crash protection but it's expensive.
Urban Kanga got a bad crash test rating.
Maxi Cosi Nomad has a very shallow belt path which means it's prone to forward anchorage in most cars.
Tinyseats and RyRy are both very heavy, so not that portable in reality, but they do fold down small and come with a travel bag.
Ride Safer Travel Vest is US certified, not EU certified and not easy (but not impossible) to buy in the UK, it's really compact, but it's not legally approved under any laws except the US one and you need to be careful of fakes. If you use it for a 15kg+ child in conjunction with a backless booster seat, then it's technically legal even in EU, and the company approve this combination, but you can't use it in conjunction with a high backed booster. I have no idea what the safety of it is, it looks so bad to me, but they do have testimonials on their site of people who had been in accidents, and it's apparently passed the US testing. Many countries have car seat exemptions for taxis, so legally, no problem using a non-approved product like this in a taxi.
They might be better than nothing, though, which is probably your other option in a taxi.
The Cosco seat is a US certified one and won't be able to be bought in the UK, or at least not easily. It's also a full sized car seat so not really portable.
Avoid 100% the "frameless" car seats sold on places that have a lot of import products like amazon, wish, ebay, aliexpress - these are sold as "portable travel car seat" but they have no crash safety features whatsoever and can be worse than nothing.