Is it happening when just one of the PC's connected to the router is playing?
It's not something i've ever even heard of as being down to an ISP's deliberate action (as I think i've said before online gaming uses absolutely minimal amounts of bandwidth, so would be about the last thing any ISP would deliberately block*).
As for routers, at number of different makes use the same basic parts, so router A might be made by Belkin, but have the same chipsets or networking chips as routers B and C made by Netgear and Linksys.
I know for example a couple of years back World of Warcraft had an issue with (I think) the drivers for Broadcom chips used in a number of routers for the WAN Connection, you would connect fine, then after a few minutes you would stop being able to interact with anything (but the connection wouldn't drop) - the answer in that case was to try different firmwares for the routers (to either earlier or later ones that used different drivers).
I've also seen a similar problem with Ultima Online where out of 3 computers in the same house, running off the same router one would "stall" whilst playing, but not lose connection - but only on the one Server (all the servers are meant to be near identical hardware), it turned out a change in the hardware at the location of one of the servers was locking out Marvel Yukon 10/100/1000 network devices, but only on the one server location (a change to another server, or fitting a very cheap realtek network card would fix it - although it was fixed at the server end after a while).
If I hadn't been able to test the connection with other machines, servers and network cards I would probably have blamed NTL (as was) for it.
Changing ISP can result in either avoiding the problem point, or because you get a different router (or ASDL modem).
I guess what i'm saying is don't be too fast to blame Virgin, as the common point of failure can still be a component of the routers (especially if you're not getting the problem at all when not using the router**), even when the routers are sold under different brands (there are only a very small number of companies that actually make the chipsets used).
*I suspect they would all prefer users to play a week of WoW than 15 minutes of full speed downloading (you're talking something under 5-10mb per hour for online gaming, unless there is a patch)
**That might even be down to a game server not being able to perform some check on your machine (punkbuster sometimes has fun with home networks).