Andrew Bridge's grandmother Valerie said: "We are delighted. It is at least something and that is all we were asking for, all we wanted was another search.
"It might not come to anything but people want them to do it and they are trying. It seemed too quick, just two days and we were saying 'if only they could do it (search) for a bit longer'.
"You never know what could happen."
The families of the sailors have travelled to London to meet foreign minister Hugh Robertson.
Leading figures from the yachting world are among more than 175,000 people who have signed an online petition supporting the campaign to resume the search.
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Rain clearing east tonight for a dry but fresher day tomorrow with plenty of sunny spells.
Heavy rain clearing east for a dry but fresher day tomorrow with some hazy sunshine.
Rain becoming heavy at times this afternoon before clearing tonight. Dry with hazy sunshine tomorrow but feeling fresher.