It's clear that if the UK have evidence of someone breaking the law then there are options available. What they're complaining about are suspects who are just being monitored as "suspicious".
But even if they'd wanted to ask e.g. Yahoo to monitor the suspects, I can't see how that would have operated. Obviously UK ISPs can identify and monitor specific people (or at least their home/mobile internet). But remote services can't tie things back to an individual[2].
Really they seem to be suggesting that anyone running a large internet service proactively monitor everything for "terrorism" and notify the relevant international authorities when this happens. From the report:
We note that several of the companies ascribed their failure to review suspicious content to the volume of material on their systems. Whilst there may be practical difficulties involved, the companies should accept they have a responsibility to notify the relevant authorities when an automatic trigger indicating terrorism is activated and allow the authorities, whether US or UK, to take the next step. We further note that several of the companies attributed the lack of monitoring to the need to protect their users’ privacy. However, where there is a possibility that a terrorist atrocity is being planned, that argument should not be allowed to prevail.
I find it hard to believe that anyone technical is suggesting this!
The MPs on the committee might not understand how impractical it is but what about the people from GCHQ who were suggesting this? Either they seriously think this is a good ide, or they're just trying to get more ammunition for increased monitoring powers within the UK.
[1] https://b1cba9b3-a-5e6631fd-s-sites.googlegroups.com/a/indep...
[2] I suppose they could use the IP address, if GCHQ did the cross referencing for changing NAT etc. But that would be impractical for some ISPs where the IP changes regularly.