Thanks Robin
Well I found the software for the modem, checked the status, which is:
Rx data Rate : 1152kbps
Tx Data Rate: 288kbps
I then ran a diagnostic check, which it fails on system test. That comes up with probable causes, the line, modem, microfilter and/or driver. So I then went and updated the modem driver, which there was an updated one. Tried the test again and got 0.128mps.
I then went to thinkbroadband.com eventually

and carried out a test, that was 0.9mps

. That’s the kind of speed I expect. So I'm assuming that the line and modem is ok, but the problem lies with BT.
I do have peer to peer software installed, but haven't used it for about 6 or so months.
I haven't checked the traffic on the line yet, but I carried out the other test, which the results are below:
C:\Documents and Settings\Compaq_Owner>tracert news.bbc.co.uk
Tracing route to newswww.bbc.net.uk [212.58.226.29]
over a maximum of 30 hops:
1 11 ms 12 ms 11 ms esr1.edinburgh5.broadband.bt.net [217.32.78.140]
2 12 ms 12 ms 12 ms 217.32.78.13
3 12 ms 15 ms 14 ms 217.41.218.1
4 14 ms 13 ms 13 ms 217.41.174.66
5 14 ms 12 ms 12 ms 217.41.218.74
6 13 ms 12 ms 12 ms 217.41.174.46
7 12 ms 13 ms 12 ms 217.47.95.114
8 13 ms 12 ms 13 ms core1-pos15-1.edinburgh.ukcore.bt.net [62.6.199.
205]
9 21 ms 20 ms 20 ms core1-pos13-0.birmingham.ukcore.bt.net [62.6.201
.25]
10 24 ms 22 ms 23 ms core1-pos5-1.ealing.ukcore.bt.net [62.6.204.218]
11 24 ms 24 ms 25 ms core1-pos1-0-0.telehouse.ukcore.bt.net [62.6.201
.82]
12 24 ms 23 ms 25 ms 194.74.65.6
13 23 ms 22 ms 23 ms 212.58.238.129
14 26 ms 25 ms 27 ms newslb12.thdo.bbc.co.uk [212.58.226.29]
Trace complete.
How anyone can make sense of that is beyond me.