I also work for a University, located in London, on the JANET network. And to be honest I never have any issues with connectivity. I can work from home from time to time and SSH and SSL sessions stay active for hours.
That being said I have seen an issue occur twice in the past 12 months when basic connectivity is fine (ICMP works) but TCP/UDP connectivity to a random selection of places (not just BBC or JANET) does not work.
When this occurs I give VM Tech Support a ring, and provided that the person answering has got some clue (once it required a second phone call) I usually explain that
- the basic network path is there, ie. ICMP ping/tracert is ok,
- TCP and UDP to random destinations appears to be dropped,
- the destinations that are non-responsive are constantly non-responsive during the problem, those that work, do work consistantly
- Using a different DNS server or IP addresses does not change matters (on both occasions the primary VM DNS server was a non-responsive destination)
- I've restarted the Cable Modem
- I've removed my router and connected my laptop directly to the cable modem
- those sites are down are OK from the same laptop using an independent internet connection (GPRS/3G) - so it's not my laptop at fault.
- I'm attached to UBR 2 in Watford

The VM tech has a look around for scheduled maintenance, checks my connection, pronounce all is OK. But usually within 10mins it appears to be cleared. Although no one ever admits anything.
I suspect that someone does a restart of soemthing upstream of me that has got a messed up network stack. There's nothing reported in the CM logs to indicate that the CM has had to renogiate.
Hope this helps in someway.