In the LIA the Thames froze. This is lazy shorthand.

Even now sometimes the UPPER reaches of the Thames freeze but not for long.

Will the Thames freeze again? Meaning the part between London and Blackfriars bridges.

Unlikely, even if LIA temperatures return: fast moving water freezes much slower than still water does and salty water freezes at a lower temperature than fresh water.

The thames Embankment was built, speeding up the river. London Bridge was rebuilt with far fewer arches/piers so sea water can flow past it much easier and faster than in the period of the Ice Fairs. something fairly drastic in meteorological terms would have to happen, would need sustained temperatures of something like -5°C for some days at least (my estimate and probably wrong. Might need colder temperatures.)

We could have a major tectonic event that dropped parts of Panama or similar that turns the Gulf of Mexico into a strait between the Pacific and Atlantic.

Or another blob of Arctic air could hit the UK/WEurope and freeze the Thames? The Beast from the East did not freeze the Thames tho minimum London temperatures hit 20°F (12°F below freezing.)

Look here: https://www.mercurynews.com/2018/02/27/british-snow-cold-beast-from-east-top-wir...

For general info on the frozen Thames and the Ice Fairs held on it see:
https://www.bbc.com/news/magazine-25862141

If something did cause the Thames to freeze again I doubt anybody will thinking of holding an Ice Fair because it would be bloody cold! REALLY cold!