Firstly it's ridiculous for anyone to say that a bus/coach from Heathrow to Southampton might take up to 5.5 hours; it's about 70 miles/110 km, motorway all the way, and takes just over an hour to drive.
Secondly a number of the major ship operators from Southampton have special trains from Waterloo station in London ("special train" here may be nothing more than a reserved carriage in the regular train), which invariably comes with transfer of you and bags from the Southampton station to shipside.
Every one of the regular express trains (several every hour) from London Waterloo to Southampton stops in the far suburbs of London at Woking, and there is a regular shuttle coach every 30 minutes from the airport terminals at Heathrow to Woking station which obviates both time and expense of going into London and coming out again.
GBP 125 may sound expensive for a car service, but by the time you have paid 3 x coach fares to Woking, plus 3 x train fares to Southampton, and finally a taxi to shipside, it's not going to come to a lot less than GBP 40 each, or 125 overall anyway, and it would be a lot less fatiguing for the 80 year old.