Sorry - I thought you were bothered about the loss of seven times £19.95 and the "computer hack" was in your mind to explain what might have happened.
To answer your question - NO - Anyone could not have hacked your computer without your knowledge. There are some people who can do this but not anyone - it's a specialist thing to do and a hacker would not do it on "spec" - £140 would hardly be worthwhile - think about it - the hacker would have taken as much as possible in one go - not several chunks of £19.95.
What appears to have happened is that you used a Bank Card to make the first payment for the supply of regular services - The supplier would need the card details to extract the first payment and to show proof to them that you actually had a bank account.
Thereafter - possibly without you realising it - the subsequent payments were on a Direct Debit (DD) basis and automatically paid out by your bank (computer to computer) with no need to refer to the number on your bank card - no need to even have a bank card.
The only safe way to stop a DD is to instruct your bank - not the payee.
Your card expiring and a new card being issued with a different number is of no consequence to a Direct Debt.
Your only realistic option to get your money back is to ask the payee - and to show that you made your wishes known to them to stop payment.
You have not been robbed - hacked or defrauded. Just a bit naive and too relaxed with your financial administration.
I am actually trying to help you - I have spent several tens of minutes in doing so - I do not feel bad at poking fun at you and will not feel ill-used if you fail to thank me for my efforts
Good luck.... Happy Christmas...
Peccavi
December 2012