6PM, wow that's one late flight home. Unfortunately Cunard are unlikely to help you onto a group transfer as those are all early morning. I am not aware of any that they do later in the day. So you may want to contact their UK offices as soon as you can to find out - they are listed under Carnival UK.
So you need to start thinking about what else you can do in case there isn't a Cunard option & are left with all your luggage.
Taxis to LHR are around £70 to £80 ($120), and a regular coach transfer runs from central Southampton and takes around 90 minutes and costs just a few £'s
It may be worth considering a taxi tour of the area (New Forest, Salisbury, Winchester, Portsmouth, or Windsor) ending up at LHR just ot pass the day.
Let me know if you want any other suggestions based on what you would feel comfortable with & I'll try my best to help.
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