It's best to keep a decent chunk of money in easily-accessible savings. The usual advice is to try to have 3-6 months of your usual income in easily accessed savings, which acts as a buffer against unexpected costs (e.g. boiler breaks down and needs replacing, significant work on your car, losing your job).
Investing in stocks and shares is normally advised as a longer-term way of saving -- for example, because the stock market goes up and down in the shorter term, it's best to look at investment in stocks and shares as being a longer-term investment. You ideally want to diversify an investment in shares -- you don't invest your money in just one or two companies.