Re: Chew it up?
What you're thinking of already exists and is commonly in use. It's known as a lift station. These are used sometimes to pump sewerage from a lower elevation to a higher elevation. They're also used to pump sewerage from a gravity-fed (no pressure) sewer system into a pressurized "forced" sewer main line (as is common here in Florida). These incorporate a wet-well chamber into which the incoming sewerage is fed, and then a pump and grinder system pumps the macerated sewerage into the outgoing line.
I'm guessing this could break up some of the softer materials. However, this would be quite costly to retrofit into an existing large sewer system, and it would increase the amount of equipment that would need to be regularly maintained and monitored by the sanitary sewer service. For a city the size of London, that would be a rather large undertaking.
Additionally, this might change the situation into problems with a multitude of individual "fatbergs" in the lift station wet wells and/or trunk lines leading to the lift stations, rather than one or two "fatbergs" in the main trunk lines of the sewer system. Also, the macerated fats and cooking oils leaving the lift stations might still be capable of congealing into the "fatberg" material, which seems to be the result of a chemical reaction (calcification of lipids from reactions with alkaline liquids).