You have to understand that the extra money payed for gas is not lost! The money has gone somewhere else, but it isn't lost!

This means that the people who get the money (the oil exporters) can (and will) spend it back into the U.K. economy (or buy bonds). If they don't the pound would not keep its value (a lot of people would not allow this to happen). So this means that the money comes back into the U.K. either way!

Only if extracting the oil requires more manual labor (more people to extract a barrel) the economy will be hurt! But since you hear every company screaming that they can not find qualified people I think that the increase in people working in the oil sector is relatively limmited (any data on this?)

Oil is traded in dollars, meaning that most of this money is crediting the US economy.

Absent revival of the UK export, more expensive oil will put downward pressure on the US pound (and on the US dollar BTW) which would mean more expensive imports leading to lower living standart.