I originally wrote a response yesterday, but forgot to post it. Others have made most of my points, leaving me with one or two...
Ive been told on FB that there are 4 main servers in the UK and that 3 are down and the reason behind all the slowdown for most the ISPs this weekend
The UK interconnections to the outside world are likely to involve one of these submarine routes:
https://www.submarinecablemap.com/Numerous routes to Holland, Belgium, France, Norway, Ireland, Canada and the US. Add in Portugal, Spain, and the Mediterranean (and on to Asia).
There's a bit more than 4 routers involved in that lot.
A lot of those routes will head into the major UK interconnection centres, which Linx run peering connectivity within. There are 10 of these places in London:
https://www.linx.net/tech-info-help/network-topology@smf22's post gives a link to BT's main peering locations (private and public), and you can see they make a lot of use of Linx's LON1 network (visible on that Linx topology page). Other ISPs are likely to connect in those locations too (incl via LON2 and LONAP), and all are likely to have either peering or transit agreements out to the international routes through those locations. For example,
Plusnet,
VM,
Sky,
TalkTalk,
B4RN.
The 10 London sites that LINX peers at are the ones that are intrinsically important to the UK's internet connectivity. Other sites (visible in the public and private peering database entries) all play their part too.
Using PeeringDB, it is also interesting to compare peering locations for
BT's US+European network with
Liberty Global's.