PC is very slow to load a new site

A customer has a PC which is connected to BT Broadband by modem rather than
router. Although it establishes a fast connection (2 Mbps), it is very slow
to load the first page on a new site. Having rebooted the PC (ie with its
DNS cache empty), it takes up to a minute to load a page such the home page
news.bbc.co.uk, with the window title taking about 30 seconds to change from
the default and the page loading gradually over the next thirty seconds.
Going to other pages on the same site, the pages load within a second or so.
This behaviour is 100% reproducable.

My first thought was that one of the two DNS servers listed in ipconfig /all
is not working, so the PC has to wait for the first one to time out before
using the second one. However, both DNS servers can be pinged, and I can
ping or do an nslookup on a brand new site and get an immediate response,
suggesting that it's not DNS name lookups which are slow.

I've run a data throughput test (to portal.f9.net.uk) and shown that the
connection is indeed achieving a throughput of nearly 2 Mbps.

I've disabled DHCP setting the DNS servers and set them manually in the
opposite order (ie the one that was DNS1 when set by DHCP is now DNS2 and
vice versa) and this makes no difference.

I've confirmed that Internet Explorer is not set to use a proxy server. The
customer acceses her email by web rather than Outlook Express, so I don't
know whether access to POP and SMTP servers is also slow or whether the
problem is confined to HTTP traffic.

Does anyone have any suggestions as to what can have gone wrong and how it
can be fixed?