"the reason the cost of living rises higher than wages rise is also because of interest and debt."
Erm... no.
Some wages increase less than inflation. Others don't. In either case, it has nothing to do with personal indebtedness.
"you pointed out cote that economic activity is because of low interest rates => more spending because of more borrowing => higher inflation"
Not quite. Economic activity will happen in any case.
When a country enters a period of slow growth (or recession) one of the tools available to counter this is to lower interest rates, which leads to:
Low interest rates > companies borrow to invest > more investments > more employment > more economic activity
Low interest rates > people borrowing for personal reasons (buying a piano, building an extension to their home, and yes, stupidly shopping for stuff they can't afford) > more economic activity
... all of which is a good thing, as long as people borrow responsibly, with a view to how much they can realistically pay back. Companies are better at this but stupid people less so.
Another tool is to increase the amount of money available (printing money, purchasing government bonds from the market etc) which, incidentally, decreases the state's indebtedness. I assume that is a good thing in your book.
Another tool is to increase government spending. Again, investments increase > more employment > more economic activity.
During a period of low interest rates and higher liquidity (lots of money in the market), it is all a balance act between boosting economic growth and keeping inflation low. Expect interest rates to start rising as soon as economic growth shows an upturn, so that we will not also see significantly higher inflation.
"so increasingly, over time, people need to borrow even more just to stay even, and stay in debt"
Not at all. In periods of economic downturn, people have the option to downsize their expenses and not borrow to live a lifestyle they no longer earn the money for.
"because cost of housing, utilities, food, consumer goods is too expensive to be able to buy outright or save for"
No. You have misunderstood. Economic downturn (because of which interest rates are lowered in the first place) means by definition that prices of things don't increase much. Low economic activity > uncertainty about the future > lower consumption > stagnant prices.
UK inflation rate is 1.9% (annual) as of January 2014. That is very low and is below Bank of England's target of 2%. It is most certainly not high or even moderate.