[anip_mambo]

Heathrow,via public transport,with quite a lot of luggage?

[Pontac]

You can do it in about 2 hours 50 minutes.Take the RailAir bus from Heathrow bus station to Reading Station, then catch the train (Great Western Service) to Cardiff Central.The RailAir bus has plenty of luggage space, and the train will be ok

[wish1765]

Well, theres two options: bus or train. I always like the bus, because if you can time it right, there are buses that take you all the way to Cardiff and no need to change (however there aren't ALOT of those at regular intervals, in my expereince). The trains are easier in a way, you can arrive at any point of the day, get onto one of the Heathrow trains to the main train station and just hop onto one of the trains that goes straight to Cardiff Central that usually depart in half hour intervals. I took the train mostly when I was moving to/fro England with all my luggage. You just have to give yourself time to get to the train (and a big recommendation, when having alot of luggage, try not to travel during the rush hours).