Sometimes it's possible via the ACARS which are posted on yahoo groups... Most ACARS come from spotters out of the UK, they are located on several places in England so they are able to see, besides all the traffic to all the British Airports, also most Atlantic crossings (which pass over the UK).
On those yahoo groups, several people are also able to have a look into the system to find out the reg.
They helped me already several times! The 'civilspotters' yahoo group is a community of about 2000 or 3000 spotters, mostly registration spotters.