Thanks, Andrew, and apologies for the radio silence. I thought I had already replied.
I think I've now satisfied myself that this isn't correlated with the VPN use. In fact, I think there have been two problems - one on the line, and one in the router.
I think the line problem manifested as long dropouts, during which the modem lost the connection (on the occasions I could be there to observe, the DSL light on the modem started flashing). After a lot of BT fiddling, those seem (touch wood) to have gone away.
The other problem continues. Occasionally, the router will lose its Internet connection, briefly. The DSL slight stays on on the modem, but for a minute or two there's no Internet access via the router. Because these outages are short it's hard to be sure, but I *think* that miniport dial-up from a PC connected directly to the modem works when the router doesn't.
A firmware upgrade (applied by my ISP) seems to have reduced the number of the short outages so that it's almost bearbale now