There is a thread on NANOG at the minute about a chap in the states having difficulty reaching certain routes over Comcast. He has the same symptoms as yourself (although his issue is a little more diverse as I believe he has several routes to travel over and only some of the routes aren't working).
Maybe you could try using a different DNS server. Change your local host DNS server to say the OpenDNS servers 208.67.222.222 and/or 208.67.220.220 (http://www.opendns.com/). I was having some issues at home with BT and changed my client DNS settings to use OpenDNS and now I have no more issues.
Admittedly I didn't look into it to much as I didn't want to give BT any more of my time so I may of been having a different problem to you. You seem to be surfing through The Carphone Warehouse so it could be a problem with them? Stabbing in the dark here, once you have gotten across the pond (hops 7-8) on the paypal.co.uk example, you spend the reaming 10 hops jumping around Level3 which seems a little weird like there is a problem with the route you are taking?
My results are below when trace routing from my home with BT, and although I never reach the end I can get on paypal.co.uk just fine;
Tracing route to paypal.co.uk [66.211.168.114] over a maximum of 30 hops:
1 81 ms 99 ms 99 ms BThomehub.home [192.168.1.254] 2 31 ms 31 ms 31 ms 217.47.93.186 3 30 ms 31 ms 31 ms 217.47.93.161 4 40 ms 42 ms 45 ms 217.47.90.10 5 30 ms 30 ms 31 ms 217.41.177.5 6 235 ms 34 ms 31 ms 217.41.177.65 7 32 ms 31 ms 30 ms 217.41.177.146 8 38 ms 36 ms 38 ms 217.41.177.34 9 40 ms 36 ms 38 ms 217.47.90.49 10 37 ms 35 ms 31 ms core1-pos12-6.faraday.ukcore.bt.net [194.72.4.12 9] 11 43 ms 47 ms 47 ms 62.172.103.29 12 43 ms 41 ms 40 ms transit1-xe0-0-0.ealing.ukcore.bt.net [62.6.200. 106] 13 44 ms 42 ms 43 ms t2c1-ge13-0-0.uk-eal.eu.bt.net [166.49.168.21] 14 43 ms 43 ms 42 ms t2c2-p3-2.uk-lon1.eu.bt.net [166.49.164.138] 15 38 ms 34 ms 36 ms t2a1-ge7-0-0.uk-lon1.eu.bt.net [166.49.135.110]
16 36 ms 35 ms 33 ms 195.66.224.130 17 40 ms 40 ms 43 ms p5-0-0d0.rar1.london-en.uk.xo.net [71.5.174.133]
18 188 ms 116 ms 118 ms p1-0-0d0.rar1.nyc-ny.us.xo.net [65.106.0.118] 19 113 ms 116 ms 149 ms te-3-1-0.rar3.nyc-ny.us.xo.net [65.106.1.18] 20 124 ms 129 ms 131 ms 207.88.14.62.ptr.us.xo.net [207.88.14.62] 21 166 ms 165 ms 173 ms 207.88.184.6.ptr.us.xo.net [207.88.184.6] 22 * * * Request timed out. 23 * * * Request timed out. 24 * * * Request timed out. 25 * * * Request timed out. 26 * * * Request timed out. 27 * * * Request timed out. 28 * * * Request timed out. 29 * * * Request timed out. 30 * * * Request timed out.
Trace complete.