which is better from LHR to Brockenhurst...bus or train?
Better in which way? Cheapest, fastest, most convenient? Which terminal will you be leaving from?
Air Rail bus to Reading station 40mins.
Reading to Brockenhurst station 1h 11mins.
If you pick your times no changes of train.
Depending on arrival time, National Express bus Heathrow-Southampton, then rail to Brockenhurst is another option. Would be cheaper, if timings are right faster too.
You might find it more convenient to take the Railair bus from Heathrow to Woking.http://www.heathrowairport.com/commuter/commuting-to-heathrow/by-bus/railair#HeathrowtoWoking
Then go to www.nationalrail.co.uk and put in for WOK > BCU. You will find frequent trains operated by >http://www.southwesttrains.co.uk