They can make all the claims that they want but if their peering to other countries and even to some providers within the uk isn't the best in that it always takes the shortest path,so not always via London then for some it would make any difference
I'm guessing by shortest path you mean lowest latency. Interconnects between ISPs use a protocol that doesn't care about latency. To achieve that is a real PITA that requires specialist software and network configuration, alongside having external-facing routers all over the place.
It's actually the field I work in, software defined networking, using things like latency and loss for real-time dynamic path selection. It can be done, however I'm not convinced any consumer-grade ISP would want to do so: it requires enterprise-grade equipment and a lot of colocation of software, either on dedicated hardware or VMs, all over the place.
I know of plenty of enterprises that have done it for hybrid WAN, and some carriers sell it as part of managed services to enterprise customers, but I'm not aware of any ISP that uses it on their network for all traffic. You'd either need a ton of hardware to handle the traffic or some method of polling all devices on the path and then dynamically reconfiguring routers in real-time to change their path selection. This is, to say the least, dicey.