There is usually a trade-off between risk and return. The higher the risk, the greater the potential return, but alongside greater risk of losing the original capital.
Savings accounts are effectively zero risk to the capital, and have a guaranteed rate of return for a period, so are very low risk, hence very low return. You can slightly improve things by going for a tax-free ISA, but the rates are lower.
Premium bonds keep your capital safe, but have a risk of zero return, which means that the capital can drop in real terms due to inflation.
Bonds are fairly secure, but are not paying well at the moment.
Stocks and shares investments are higher risk - you can lose the capital, however even within these you can vary the risk. Investing in individual shares is the highest risk, funds decrease the risk. Some funds invest in higher risk areas such as smaller companies or emerging markets, others in lower risk areas such as UK or European blue-chip companies. Any investment of this type is likely to fluctuate - growth isn't continuous like it is with a savings account, however the idea is that over the longer term you see larger levels of growth.
The other thing that comes into play is a balanced portfolio - you don't want all your eggs in one basket so the normal approach is spreading it around, based on your attitude to risk, how much of it you can afford to lose in the worst case vs how much growth you want to potentially achieve, and whether you can cope with it going down as well as up.
I don't have the time or knowledge to construct a decent portfolio, so I use an independent financial advisor. We use Investment Sense, who are national and I have always found very clear and helpful. They are also free for the first consultation, and their fee structure is declared up front with no hidden extras. They do not simply want your money - they form a view as to how much should be where to achieve balance, ie cash type accounts vs. investments; they want to invest the investable bit. They have also done a good job of identifying which funds should be switched when, and do the lot from an annual meeting, sometimes visiting us, sometimes by Skype, and then by email, with email confirmation from us if we want to accept their recommendations. We have achieved significantly higher returns than you would expect from a savings account - the first time round, enough to step up from our previous small house with small garden to this place with 6.5 acres, and when we had got over the first financial hump, we have started a second time around which is doing nicely.
Alec